Gregoire Misguich home page

Publications and preprints

Almost all my papers and preprints are on the on the arXiv archive, to get the list click here.

For published papers (and associated bibliometry), you can also look at ResearcherID: K-1781-2015

Aletrnatively you can see my publications on google scholar.



Publications (last update: Dec. 22nd, 2020)

[68] "DMRG study of FQHE systems in the open cylinder geometry "
Grégoire Misguich and Thierry Jolicoeur .
arXiv:2012.03000
Proceedings of the International Conference on Computer Simulation in Physics and beyond (CSP2020), October 12-16, 2020, Moscow, Russia

Abstract: The study of the fractional quantum Hall liquid state of two-dimensional electrons requires a non-perturbative treatment of interactions. It is possible to perform exact diagonalizations of the Hamiltonian provided one considers only a small number of electrons in an appropriate geometry. Many insights have been obtained in the past from considering electrons moving on a sphere or on a torus. In the Landau gauge it is also natural to impose periodic boundary conditions in only one direction, the cylinder geometry. The interacting problem now looks formally like a one-dimensional problem that can be attacked by the standard DMRG algorithm. We have studied the efficiency of this algorithm to study the ground state properties of the electron liquid at lowest Landau level filling factor ν=1/3 when the interactions are truncated to the two most important repulsive hard-core components. Use of finite-size DMRG allows us to conclude that the ground state is a compressible two-electron bubble phase in agreement with previous Hartree-Fock calculations. We discuss the treatment of Coulomb interactions in the cylinder geometry. To regularize the long-distance behavior of the Coulomb potential, we compare two methods: using a Yukawa potential or forbidding arbitrary long distances by defining the interelectron distance as the chord distance through the cylinder. This allows us to observe the Wigner crystal state for small filling factor.


[67] "Generalized hydrodynamics in complete box-ball system for Uq(sln) "
Atsuo Kuniba, Grégoire Misguich, Vincent Pasquier .
arXiv:2011.08052
Submitted to SciPost Physics

Abstract: We introduce the complete box-ball system (cBBS), which is an integrable cellular automaton on 1D lattice associated with the quantum group Uq(slˆn). Compared with the conventional (n−1)-color BBS, it enjoys a remarkable simplification that scattering of solitons is totally diagonal. We also introduce a randomized cBBS and study its non-equilibrium behavior by thermodynamic Bethe ansatz and generalized hydrodynamics. Excellent agreement is demonstrated between theoretical predictions and numerical simulation on the density plateaux generated from domain wall initial conditions including their diffusive broadening.


[66] "Bubble phase at ν=1/3 for a spinless hollow-core interaction "
Grégoire Misguich, Thierry Jolicoeur, Takahiro Mizusaki .
Phys. Rev. B 102, 245107 (2020). (pdf)
Abstract: We investigate fractional quantum Hall states for model interactions restricted to a repulsive hard core. When the hard core excludes relative angular momentum m=1 between spinless electrons the ground state at Landau level filling factor ν=13 is known to be exactly given by the Laughlin wave function. When we exclude relative angular momentum 3 only, Wójs, Quinn, and Yi have suggested the appearance of a liquid state with non-Laughlin correlations. We study this special hard-core interaction at filling factor 13 on the sphere, torus, and cylinder geometry. An analysis of the charged and neutral gaps on the sphere geometry points to a gapless state. On the torus geometry the projected static structure factor has a two-peak feature pointing to one-dimensional density ordering. To clarify the nature of the ground state we perform extended density matrix renormalization group studies on the cylinder geometry for up to 30 particles. The pair correlation function allows us to conclude that the ground state is a two-particle bubble phase.


[65] "Generalized hydrodynamics in box-ball system "
Atsuo Kuniba, Grégoire Misguich, Vincent Pasquier .
J. Phys. A: Math. Theor. 53 404001 (2020) (pdf)
Abstract: Box-ball system (BBS) is a prominent example of integrable cellular automata in one dimension connected to quantum groups, Bethe ansatz, ultradiscretization, tropical geometry and so forth. In this paper we study the generalized Gibbs ensemble of BBS soliton gas by thermodynamic Bethe ansatz and generalized hydrodynamics. The results include the solution to the speed equation for solitons, an intriguing connection of the effective speed with the period matrix of the tropical Riemann theta function, an explicit description of the density plateaux that emerge from domain wall initial conditions including their diffusive corrections.


[64] "Correlation-induced steady states and limit cycles in driven dissipative quantum systems "
Haggai Landa, Marco Schiró, Grégoire Misguich .
Phys. Rev. B 102, 064301 (2020) (pdf)
Abstract: We study a driven-dissipative model of spins one-half (qubits) on a lattice with nearest-neighbor interactions. Focusing on the role of spatially extended spin-spin correlations in determining the phases of the system, we characterize the spatial structure of the correlations in the steady state, as well as their temporal dynamics. In dimension one we use essentially exact matrix-product-operator simulations on large systems, and pushing these calculations to dimension two, we obtain accurate results on small cylinders. We also employ an approximation scheme based on solving the dynamics of the mean field dressed by the feedback of quantum fluctuations at leading order. This approach allows us to study the effect of correlations in large lattices with over one hundred thousand spins, as the spatial dimension is increased up to five. In dimension two and higher we find two new states that are stabilized by quantum correlations and do not exist in the mean-field limit of the model. One of these is a steady state with mean magnetization values that lie between the two bistable mean-field values and whose correlation functions have properties reminiscent of both. The correlation length of the new phase diverges at a critical point, beyond which we find emerging a new limit cycle state with the magnetization and correlators oscillating periodically in time.


[63] "Multistability of Driven-Dissipative Quantum Spins "
Haggai Landa, Marco Schiró, and Grégoire Misguich .
Phys. Rev. Lett. 124, 043601 (2020) (pdf)
Abstract: We study the dynamics of lattice models of quantum spins one-half, driven by a coherent drive and subject to dissipation. Generically the mean-field limit of these models manifests multistable parameter regions of coexisting steady states with different magnetizations. We introduce an efficient scheme accounting for the corrections to mean field by correlations at leading order, and benchmark this scheme using high-precision numerics based on matrix-product operators in one- and two-dimensional lattices. Correlations are shown to wash the mean-field bistability in dimension one, leading to a unique steady state. In dimension two and higher, we find that multistability is again possible, provided the thermodynamic limit of an infinitely large lattice is taken first with respect to the longtime limit. Variation of the system parameters results in jumps between the different steady states, each showing a critical slowing down in the convergence of perturbations towards the steady state. Experiments with trapped ions can realize the model and possibly answer open questions in the nonequilibrium many-body dynamics of these quantum systems, beyond the system sizes accessible to present numerics.


[62] "Concurrence and Quantum Discord in the Eigenstates of Chaotic and Integrable Spin Chains "
Atefeh Ashouri, Saeed Mahdavifar, Grégoire Misguich and Javad Vahedi .
Annalen der Physik, 532, 1900515 (2020)
Abstract: There has been some substantial research about the connections between quantum chaos and quantum correlations in many‐body systems. This paper discusses a specific aspect of correlations in chaotic spin models, through concurrence (CC) and quantum discord (QD). Numerical results obtained in the quantum chaos regime and in the integrable regime of spin‐1/2 chains are compared. The CC and QD between nearest‐neighbor pairs of spins are calculated for all energy eigenstates. The results show that, depending on whether the system is in a chaotic or integrable regime, the distribution of CC and QD are markedly different. On the other hand, in the integrable regime, states with the largest CC and QD are found in the middle of the spectrum, in the chaotic regime, the states with the strongest correlations are found at low and high energies at the edges of spectrum. Finite‐size effects are analyzed, and some of the results are discussed in the light of the eigenstate thermalization hypothesis.


[61] "Domain wall problem in the quantum XXZ chain and semiclassical behavior close to the isotropic point "
Grégoire Misguich, Nicolas Pavloff, Vincent Pasquier .
SciPost Phys. 7, 025 (2019) (pdf)
Abstract: Using We study the dynamics of a spin-1/2 XXZ chain which is initially prepared in a domain-wall state. We compare the results of time-dependent Density Matrix Renormalization Group simulations with those of an effective description in terms of a classical anisotropic Landau-Lifshitz (LL) equation. Numerous quantities are analyzed: magnetization (x, y and z components), energy density, energy current, but also some spin-spin correlation functions or entanglement entropy in the quantum chain. Without any adjustable parameter a quantitative agreement is observed between the quantum and the LL problems in the long time limit, when the models are close to the isotropic point. This is explained as a consequence of energy conservation. At the isotropic point the mapping between the LL equation and the nonlinear Schr\"odinger equation is used to construct a variational solution capturing several aspects of the problem.


[60] "Out-of-equilibrium transport in the interacting resonant level model: Surprising relevance of the boundary sine-Gordon model "
Kemal Bidzhiev, Grégoire Misguich, and Hubert Saleur .
Phys. Rev. B 100, 075157 (2019) (pdf)
Abstract: Using time-dependent density matrix renormalization group calculations we study the transport properties (I−V curves and shot noise) of the interacting resonant level model (IRLM) in a large range of the interaction parameter U, in the scaling limit. We find that these properties can be described remarkably well by those of the boundary sine-Gordon model (BSG), which are known analytically [Fendley et al., Phys. Rev. B 52, 8934 (1995).]. We argue that the two models are nevertheless in different universality classes out-of-equilibrium: this requires a delicate discussion of their infrared (IR) properties (i.e., at low bias), where we prove in particular that the effective tunneling charge is e in the infrared regime of the IRLM (except at the self-dual point where it jumps to 2e), while it is known to be a continuously varying function of U in the BSG. This behavior is confirmed by careful analysis of the numerical data in the IR. The remarkable agreement of the transport properties, especially in the crossover region, remains however unexplained.


[59] "Dynamics of the spin-1/2 Heisenberg chain initialized in a domain-wall state "
Grégoire Misguich, Kirone Mallick, and P. L. Krapivsky .
Phys. Rev. B 96, 195151 (2017) (pdf)
Abstract: We study the dynamics of an isotropic spin-1/2 Heisenberg chain starting in a domain-wall initial condition where the spins are initially up on the left half-line and down on the right half-line. We focus on the long-time behavior of the magnetization profile. We perform extensive time-dependent density-matrix renormalization-group simulations (up to t=350) and find that the data are compatible with a diffusive behavior. Subleading corrections decay slowly blurring the emergence of the diffusive behavior. We also compare our results with two alternative scenarios: superdiffusive behavior and enhanced diffusion with a logarithmic correction. We finally discuss the evolution of the entanglement entropy.


[58] "Out-of-equilibrium dynamics in a quantum impurity model: numerics for particle transport and entanglement entropy "
Kemal Bidzhiev and Grégoire Misguich .
Phys. Rev. B 96, 195117 (2017) (pdf)
Abstract: We investigate the out-of-equilibrium properties of a simple quantum impurity model, the interacting resonant level model. We focus on the scaling regime, where the bandwidth of the fermions in the leads is larger than all the other energies, so that the lattice and the continuum versions of the model become equivalent. Using time-dependent density matrix renormalization group simulations initialized with states having different densities in the two leads, we extend the results of Boulat, Saleur, and Schmitteckert [Phys. Rev. Lett. 101, 140601 (2008)] concerning the current-voltage (I−V) curves, for several values of the interaction strength U. We estimate numerically the Kondo scale TB and the exponent b(U) associated to the tunneling of the fermions from the leads to the dot. Next, we analyze the quantum entanglement properties of the steady states. We focus in particular on the entropy rate α, describing the linear growth with time of the bipartite entanglement in the system. We show that, as for the current, α/TB is described by some function of U and of the rescaled bias V/TB. Finally, the spatial structure of the entropy profiles is discussed.


[57] "Finite-size scaling of the Shannon-Rényi entropy in two-dimensional systems with spontaneously broken continuous symmetry "
Grégoire Misguich, Vincent Pasquier, Masaki Oshikawa .
Phys. Rev. B 95, 195161 (2017) (pdf)
Abstract: We study the scaling of the (basis dependent) Shannon entropy for two-dimensional quantum antiferromagnets with Néel long-range order. We use a massless free-field description of the gapless spin wave modes and phase space arguments to treat the fact that the finite-size ground state is rotationally symmetric, while there are degenerate physical ground states which break the symmetry. Our results show that the Shannon entropy (and its Rényi generalizations) possesses some universal logarithmic term proportional to the number NNG of Nambu-Goldstone modes. In the case of a torus, we show that Sn>1≃O(N)+(NNG/4)*n/(n−1)*logN and S1≃O(N)−(NNG/4)*logN, where N is the total number of sites and n the Rényi index. The result for n>1 is in reasonable agreement with the quantum Monte Carlo results of Luitz et al. [Phys. Rev. Lett. 112, 057203 (2014)], and qualitatively similar to those obtained previously for the entanglement entropy. The Shannon entropy of a line subsystem (embedded in the two-dimensional system) is also considered. Finally, we present some density-matrix renormalization group (DMRG) calculations for a spin-1/2 XY model on the square lattice in a cylinder geometry. These numerical data confirm our findings for logarithmic terms in the n=∞ Rényi entropy (also called −log pmax). They also reveal some universal dependence on the cylinder aspect ratio, in good agreement with the fact that, in that case, pmax is related to a non-compact free-boson partition function in dimension 1+1.


[56] "Inverse participation ratios in the XXZ spin chain "
Grégoire Misguich, Vincent Pasquier, Jean-Marc Luck .
Phys. Rev. B 94, 155110 (2016) (pdf)
Abstract: We investigate numerically the inverse participation ratios in a spin-1/2 XXZ chain, computed in the ``Ising'' basis (i.e., eigenstates of σzi). We consider in particular a quantity T, defined by summing the inverse participation ratios of all the eigenstates in the zero magnetization sector of a finite chain of length N, with open boundary conditions. From a dynamical point of view, T is proportional to the stationary return probability to an initial basis state, averaged over all the basis states (initial conditions). We find that T exhibits an exponential growth, T∼exp(aN), in the gapped phase of the model and a linear scaling, T∼N, in the gapless phase. These two different behaviors are analyzed in terms of the distribution of the participation ratios of individual eigenstates. We also investigate the effect of next-nearest-neighbor interactions, which break the integrability of the model. Although the massive phase of the non-integrable model also has T∼exp(aN), in the gapless phase T appears to saturate to a constant value.


[55] "Flux quench in a system of interacting spinless fermions in one dimension "
Yuya O. Nakagawa, Grégoire Misguich, Masaki Oshikawa .
Phys. Rev. B 93, 174310 (2016) (pdf)
Abstract: We study a quantum quench in a one-dimensional spinless fermion model (equivalent to the XXZ spin chain), where a magnetic flux is suddenly switched off. This quench is equivalent to imposing a pulse of electric field and therefore generates an initial particle current. This current is not a conserved quantity in the presence of a lattice and interactions, and we investigate numerically its time evolution after the quench, using the infinite time-evolving block decimation method. For repulsive interactions or large initial flux, we find oscillations that are governed by excitations deep inside the Fermi sea. At long times we observe that the current remains nonvanishing in the gapless cases, whereas it decays to zero in the gapped cases. Although the linear response theory (valid for a weak flux) predicts the same long-time limit of the current for repulsive and attractive interactions (relation with the zero-temperature Drude weight), larger nonlinearities are observed in the case of repulsive interactions compared with that of the attractive case.


[54] "Phase diagram of an extended quantum dimer model on the hexagonal lattice "
Thiago Schlittler, Thomas Barthel, Grégoire Misguich, Julien Vidal, and Rémy Mosseri .
Phys. Rev. Lett 115, 217202 (2015) (pdf)
Abstract: We introduce a quantum dimer model on the hexagonal lattice that, in addition to the standard three-dimer kinetic and potential terms, includes a competing potential part counting dimer-free hexagons. The zero-temperature phase diagram is studied by means of quantum Monte Carlo simulations, supplemented by variational arguments. It reveals some new crystalline phases and a cascade of transitions with rapidly changing flux (tilt in the height language). We analyze perturbatively the vicinity of the Rokhsar-Kivelson point, showing that this model has the microscopic ingredients needed for the "devil's staircase" scenario [E. Fradkin et al., Phys. Rev. B 69, 224415 (2004)], and is therefore expected to produce fractal variations of the ground-state flux.


[53] "Entanglement and Shannon entropies in low-dimensional quantum systems "
Grégoire Misguich .
Habilitation thesis, Université P. et M. Curie, June 2014 (pdf)
Abstract in French, but the main document is in English.

Abstract: La première partie de ce mémoire traite de l'intrication quantique (entropie de Von Neumann) dans certains systèmes bidimensionnels. Il s'agit de fonctions d'onde de type Rokhsar-Kivelson (RK), construites à partir des poids de Boltzmann d'un modèle classique (modèle de dimères, de vertex ou de spins d'Ising par exemple). Nous montrons comment le spectre des matrices densité réduites de ces états s'obtient à partir des probabilités du modèle classique sous-jacent. Cette observation permet de calculer numériquement l'entropie d'intrication dans de grands systèmes, et en particulier de tester la présence de constantes sous-dominantes universelles dans le cas d'un liquide (de dimères) topologique de type Z2 (construction de Kitaev-Preskill & Levin-Wen) et dans le cas d'une fonction d'onde critique (dimères sur réseaux bipartites). Si le système est un cylindre infiniment long et que le sous-système considéré est un demi-cylindre infini, le spectre de la matrice densité réduite peut se calculer plus simplement encore, par matrice de transfert. L'entropie d'intrication entre les deux moitiés du système apparaît alors comme l'entropie de Shannon associée aux probabilités des différentes configurations des degrés de liberté qui se trouvent à la frontière (un cercle). Ceci nous conduit à considérer l'entropie de Shannon (et ses généralisations de type Rényi) d'une fonction d'onde à N corps en tant que telle indépendamment de son lien éventuel avec l'intrication quantique d'un état RK en dimension supérieure. Nous étudions les contributions universelles de cette entropie dans trois cas: 1) les liquides de Tomonaga-Luttinger, cadre dans lequel nous établissons un lien entre l'entropie de Shannon-Rényi et des problèmes de théories conformes avec bords, et calculons exactement les termes universels de l'entropie en fonction du paramètre de Luttinger et de l'indice de Rényi; 2) la chaîne d'Ising critique en champ transverse, pour laquelle nos simulations numériques montrent la présence d'une transition de phase à n=1 (indice de Rényi), qui reste mal comprise théoriquement, et pour laquelle une approche par méthode des répliques semble inadaptée; et enfin 3) des systèmes bidimensionnels avec symétrie continue spontanément brisée, où nous expliquons par un argument de champ libre (et de tour d'états) la présence de termes en log(L) dans l'entropie, comme récemment observé par simulations Monte-Carlo quantique.


[52] "Ising anyons with a string tension "
Marc Daniel Schulz, Sébastien Dusuel, Grégoire Misguich, Kai Phillip Schmidt, and Julien Vidal .
Phys. Rev. B 89, 201103(R) (2014) (pdf)
Abstract: We consider the string-net model on the honeycomb lattice for Ising anyons in the presence of a string tension. This competing term induces a nontrivial dynamics of the non-Abelian anyonic quasiparticles and may lead to a breakdown of the topological phase. Using high-order series expansions and exact diagonalizations, we determine the robustness of this doubled Ising phase, which is found to be separated from two gapped phases. An effective quantum dimer model emerges in the large tension limit, giving rise to two different translation symmetry-broken phases. Consequently, we obtain four transition points, two of which are associated with first-order transitions whereas the two others are found to be continuous and provide examples of recently proposed Bose condensation for anyons.


[51] "Non-equilibrium steady states in the quantum XXZ spin chain "
Thiago Sabetta, Grégoire Misguich .
Phys. Rev. B 88, 245114 (2013) (pdf)
Abstract: We investigate the dynamics of a critical XXZ spin-1/2 chain prepared in an inhomogeneous initial state with different magnetizations on the left and right halves. We simulate the real-time evolution using the time-evolving block decimation (TEBD) method. We follow the front propagation by measuring the magnetization and entanglement entropy profiles, and we focus on the situation where the initial state is not fully polarized. At long times, as in the free fermion case (T. Antal et al. 1999), a large central region develops where correlations become time-independent and translation invariant. The shape and speed of the fronts is studied numerically and we evaluate the stationary current as a function of initial magnetic field and as a function of the anisotropy \Delta. We compare the results with the conductance of a Tomonaga-Luttinger liquid, and with the exact free-fermion solution at Delta=0. We also investigate the two-point correlations in the stationary region and find a good agreement with the "twisted" form obtained by J. Lancaster and A. Mitra (2010) using bosonization. Some deviations are nevertheless observed for strong currents.


[50] "Time-reversal-symmetry-breaking chiral spin liquids: a projective symmetry group approach of bosonic mean-field theories "
Laura Messio, Claire Lhuillier, Grégoire Misguich .
Phys. Rev. B 87, 125127 (2013) (pdf)
Abstract: Projective symmetry groups (PSG) are the mathematical tools which allow to list and classify mean-field spin liquids (SL) based on a parton construction. The seminal work of Wen and its subsequent extension to bosons by Wang and Vishwanath concerned the so-called symmetric SL: i.e. states that break neither lattice symmetries nor time reversal invariance. Here we generalize this approach to chiral (time reversal symmetry breaking) SL described in a Schwinger boson mean-field approach. A special emphasis is put on frustrated lattices (triangular and kagome lattices), where the possibility of a chiral SL ground state has recently been discussed. The PSG approach is detailed for the triangular lattice case. Results for other lattices are given in the appendices. The physical significance of gauge invariant quantities called fluxes is discussed both in the classical limit and in the quantum SL and their expressions in terms of spin observables are given.


[49] "Schwinger boson mean field theory: numerics for the energy landscape and gauge excitations in two-dimensional antiferromagnets "
Grégoire Misguich .
Phys. Rev. B 86, 245132 (2012) (pdf)
Abstract: We perform some systematic numerical search for Schwinger boson mean field states on the square, triangular and kagome clusters. We look for possible inhomogeneous ground states as well as low-energy excited saddle points. The spectrum of the Hessian is also computed for each solution. On the square lattice we find gapless U(1) gauge modes in the non-magnetic phase. In the Z2 liquid phase of the triangular lattice we identify the topological degeneracy as well as vison states. The energy landscape on kagome lattices shows tiny energy scales and we discuss its relation to classical planar states.


[48] "Competing Valence Bond Crystals in the Kagome Quantum Dimer Model "
Didier Poilblanc and Grégoire Misguich .
Phys. Rev. B 84, 214401 (2011) (pdf)
Abstract: The singlet dynamics which plays a major role in the physics of the spin-1/2 Quantum Heisenberg Antiferromagnet (QHAF) on the Kagome lattice can be approximately described by projecting onto the nearest-neighbor valence bond (NNVB) singlet subspace. We re-visit here the effective Quantum Dimer Model which originates from the latter NNVB-projected Heisenberg model via a non-perturbative Rokhsar-Kivelson-like scheme. By using Lanczos exact diagonalisation on a 108-site cluster supplemented by a careful symmetry analysis, it is shown that a previously-found 36-site Valence Bond Crystal (VBC) in fact competes with a new type of 12-site "resonating-columnar" VBC. The exceptionally large degeneracy of the GS multiplets (144 on our 108-site cluster) might reflect the proximity of the Z2 dimer liquid. Interestingly, these two VBC "emerge" in {\it different topological sectors}. Implications for the interpretation of numerical results on the QHAF are outlined.


[47] "Rényi entanglement entropies in quantum dimer models : from criticality to topological order "
Jean-Marie Stéphan, Grégoire Misguich and Vincent Pasquier .
J. Stat. Mech. (2012) P02003 (pdf)
Abstract: Thanks to Pfaffian techniques, we study the Rényi entanglement entropies and the entanglement spectrum of large subsystems for two-dimensional Rokhsar-Kivelson wave functions constructed from a dimer model on the triangular lattice. By including a fugacity t on some suitable bonds, one interpolates between the triangular lattice (t=1) and the square lattice (t=0). The wave function is known to be a massive Z2 topological liquid for t>0 whereas it is a gapless critical state at t=0. We mainly consider two geometries for the subsystem: that of a semi-infinite cylinder, and the disk-like setup proposed by Kitaev and Preskill [Phys. Rev. Lett. 96, 110404 (2006)]. In the cylinder case, the entropies contain an extensive term -- proportional to the length of the boundary -- and a universal sub-leading constant sn(t). Fitting these cylinder data (up to a perimeter of L=32 sites) provides sn with a very high numerical accuracy (10^{-9} at t=1 and 10^{-6} at t=0.5). In the topological Z2 liquid phase we find sn(t>0)=-ln 2, independent of the fugacity t and the Rényi parameter n. At t=0 we recover a previously known result, sn(t=0)=-(1/2)\ln(n)/(n-1) for n<1 and sn(t=0)=-ln(2)/(n-1) for n>1. In the disk-like geometry -- designed to get rid of the boundary contributions -- we find an entropy sKPn(t>0)=-\ln 2 in the whole massive phase whatever n>0, in agreement with the result of Flammiaet al. [Phys. Rev. Lett. 103, 261601 (2009)]. Some results for the gapless limit RKPn(t\to 0) are discussed.


[46] "Phase transition in the Rényi-Shannon entropy of Luttinger liquids "
Jean-Marie Stéphan, Grégoire Misguich, Vincent Pasquier .
Phys. Rev. B 84, 195128 (2011) (pdf)
Rejected from PRL :-(

Abstract: The Rényi-Shannon entropy associated to critical quantum spins chain with central charge c=1 is shown to have a phase transition at some value nc of the Rényi parameter n which depends on the Luttinger parameter (or compactification radius R). Using a new replica-free formulation, the entropy is expressed as a combination of single-sheet partition functions evaluated at n-dependent values of the stiffness. The transition occurs when a vertex operator becomes relevant at the boundary. Our numerical results (exact diagonalizations for the XXZ and J1-J2 models) are in agreement with the analytical predictions: above nc=4/R2 the subleading and universal contribution to the entropy is \ln(L)(R2-1)/(4n-4) for open chains, and \ln(R)/(1-n) for periodic ones (R=1 at the free fermion point). The replica approach used in previous works fails to predict this transition and turns out to be correct only for nc. From the point of view of two-dimensional Rokhsar-Kivelson states, the transition reveals a rich structure in the entanglement spectra.


[45] "Lattice symmetries and regular states in classical frustrated antiferromagnets "
Laura Messio, Claire Lhuillier, Grégoire Misguich .
Phys. Rev. B 83, 184401 (2011) (pdf)
Editors's suggestion

Abstract: We consider some classical and frustrated lattice spin models with global O(3) spin symmetry. There is no general analytical method to find a ground-state if the spin dependence of the Hamiltonian is more than quadratic (i.e. beyond the Heisenberg model) and/or if the lattice has more than one site per unit cell. To deal with these situations, we introduce a family of variational spin configurations, dubbed "regular states", which respect all the lattice symmetries modulo global O(3) spin transformations (rotations and/or spin flips). The construction of these states is explicited through a group theoretical approach, and all the regular states on the square, triangular, honeycomb and kagome lattices are listed. Their equal time structure factors and powder-averages are shown for comparison with experiments. All the well known Néel states with 2 or 3 sublattices appear amongst regular states on various lattices, but the regular states also encompass exotic non-planar states with cubic, tetrahedral or cuboctahedral geometry of the T=0 order parameter. Whatever the details of the Hamiltonian (with the same symmetry group), a large fraction of these regular states are energetically stationary with respect to small deviations of the spins. In fact these regular states appear as exact ground-states in a very large range of parameter space of the simplest models that we have been looking at. As examples, we display the variational phase diagrams of the J1-J2-J3 Heisenberg model on all the previous lattices as well as that of the J1-J2-K ring-exchange model on square and triangular lattices.


[44] "Geometric entanglement of critical XXZ and Ising chains and Affleck-Ludwig boundary entropies "
Jean-Marie Stéphan, Grégoire Misguich, Fabien Alet .
Phys. Rev. B 82, 180406(R) (2010) (pdf)
Abstract: We study the geometrical entanglement of the XXZ chain in its critical regime. Recent numerical simulations [Q.-Q. Shi, R. Orus, J. O. Fjaerestad and H.-Q Zhou, New J. Phys. 12, 025008 (2010)] indicate that it scales linearly with system size, and that the first subleading correction is constant, which was argued to be possibly universal. In this work, we confirm the universality of this number, by relating it to the Affleck-Ludwig boundary entropy corresponding to a Neumann boundary condition for a free compactified field. We find that the subleading constant is a simple function of the compactification radius, in agreement with the numerics. As a further check, we compute it exactly on the lattice at the XX point. We also discuss the case of the Ising chain in transverse field and show that the geometrical entanglement is related to the Affleck-Ludwig boundary entropy associated to a ferromagnetic boundary condition.


[43] "Rényi entropy of a line in two-dimensional Ising models "
Jean-Marie Stéphan, Grégoire Misguich, Vincent Pasquier .
Phys. Rev. B 82, 125455 (2010) (pdf)
Abstract: We consider the two-dimensional (2d) Ising model on a infinitely long cylinder and study the probabilities pi to observe a given spin configuration i along a circular section of the cylinder. These probabilities also occur as eigenvalues of reduced density matrices in some Rokhsar-Kivelson wave-functions. We analyze the subleading constant to the Rényi entropy Rn=1/(1-n) ln (sumi pin) and discuss its scaling properties at the critical point. Studying three different microscopic realizations, we provide numerical evidence that it is universal and behaves in a step-like fashion as a function of n, with a discontinuity at the Shannon point n=1. As a consequence, a field theoretical argument based on the replica trick would fail to give the correct value at this point. We nevertheless compute it numerically with high precision. Two other values of the Rényi parameter are of special interest: n=1/2 and n=infinity are related in a simple way to the Affleck-Ludwig boundary entropies associated to free and fixed boundary conditions respectively.


[42] "Quantum spin liquids and fractionalization "
Gregoire Misguich .
Chapter in "Introduction to Frustrated Magnetism", C. Lacroix, F. Mila and P. Mendels (Eds.), Springer 2011. (pdf)
Notes for some lectures given at the school on "Highly frustrated magnetism" (Trieste, August 2007). 29 pages.

Abstract: This chapter discusses quantum antiferromagnets which do not break any symmetries at zero temperature -- also called spin liquids -- and focuses on lattice spin models with Heisenberg-like (i.e. SU(2)-symmetric) interactions in dimensions larger than one. We begin by discussing the Lieb-Schultz-Mattis theorem and its recent extension to D>1 by Hastings (2004), which establishes an important distinction between spin liquids with an integer and with a half-integer spin per unit cell. Spin liquids of the rst kind, band insulators, can often be understood by elementary means, whereas the latter, Mott insulators, are more complex (featuring topological order) and support spin-1/2 excitations (spinons). The fermionic formalism (Afleck and Marston, 1988) is described and the effect of fluctuations about mean-field solutions, such as the possible creation of instabilities, is discussed in a qualitative way. In particular, we explain the emergence of gauge modes and their relation to fractionalization. The concept of the projective symmetry group (X.-G. Wen, 2002) is introduced, with the aid of some examples. Finally, we present the phenomenology of (gapped) short-ranged resonating-valence-bond spin liquids, and make contact with the fermionic approach by discussing their description in terms of a uctuating Z2 gauge field. Some recent references are given to other types of spin liquid, including gapless ones.


[41] "Shannon and entanglement entropies of one- and two-dimensional critical wave functions "
Jean-Marie Stéphan, Shunsuke Furukawa, Grégoire Misguich, Vincent Pasquier .
Phys. Rev. B 80, 184421 (2009) (pdf)
Abstract: We study the Shannon entropy of the probability distribution resulting from the ground-state wave function of a one-dimensional quantum model. This entropy is related to the entanglement entropy of a Rokhsar-Kivelson-type wave function built from the corresponding two-dimensional classical model. In both critical and massive cases, we observe that it is composed of an extensive part proportional to the length of the system and a subleading universal constant S0. In c=1 critical systems (Tomonaga-Luttinger liquids) , we find that S0 is a simple function of the boson compactification radius. This finding is based on a field-theoretical analysis of the Dyson-Gaudin gas related to dimer and Calogero-Sutherland models. We also performed numerical demonstrations in the dimer models and the spin-1/2 XXZ chain. In a massive (crystal) phase, S0 is related to the ground-state degeneracy. We also examine this entropy in the Ising chain in a transverse field as an example showing a c=1/2 critical point.


[40] "Comment on "Regional Versus Global Entanglement in Resonating-Valence-Bond States" "
Fabien Alet, Daniel Braun, Grégoire Misguich .
Phys. Rev. Lett. 101, 248901 (2008) (pdf)
Abstract: In a recent Letter [Phys. Rev. Lett. 99, 170502 (2007); quant-ph/0703227], Chandran and coworkers study the entanglement properties of valence bond (VB) states. Their main result is that VB states do not contain (or only an insignificant amount of) two-site entanglement, whereas they possess multi-body entanglement. Two examples ("RVB gas and liquid") are given to illustrate this claim, which essentially comes from a lower bound derived for spin correlators in VB states. We show in this Comment that (i) for the "RVB liquid" on the square lattice, the calculations and conclusions of Chandran et al. are incorrect. (ii) A simple analytical calculation gives the exact value of the correlator for the "RVB gas", showing that the bound found by Chandran et al. is tight. (iii) The lower bound for spin correlators in VB states is equivalent to a celebrated result of Anderson dating from more than 50 years ago.


[39] "Quantum spin liquids "
Gregoire Misguich .
arXiv:0809.2257
Lectures given at the Les Houches summer school on "Exact Methods in Low-dimensional Statistical Physics and Quantum Computing" (July 2008)

Abstract: These notes are an introduction to a few selected theoretical ideas in the field of quantum spin liquids: classical zero modes and breakdown of the 1/S expansion, the Lieb-Schultz-Mattis-Hastings theorem and Oshikawa's argument, the short-ranged resonating valence-bond picture, large-N limit (Schwinger bosons) and Z2 gauge theory.


[38] "Correlations and order parameter at a Coulomb-crystal phase transition in a three-dimensional dimer model "
Gregoire Misguich, Vincent Pasquier, Fabien Alet .
Phys. Rev. B 78, 100402(R) (2008) (pdf)
Abstract: The three-dimensional classical dimer model with interactions shows an unexpected continuous phase transition between an ordered dimer crystal and a Coulomb liquid. A detailed analysis of the critical dimer and monomer correlation functions points to a subtle interplay between the fluctuations of the crystal order parameter and the "magnetic" degrees of freedom present in the Coulomb phase. The distribution probability of the crystal order parameter suggests an emerging continuous O(3) symmetry at the critical point.


[37] "Thermal destruction of chiral order in a two-dimensional model of coupled trihedra "
Laura Messio, Jean-Christophe Domenge, Claire Lhuillier, Laurent Pierre, Pascal Viot, and Gregoire Misguich .
Phys. Rev. B 78, 054435 (2008) (pdf)
Abstract: We introduce a minimal model describing the physics of classical two-dimensional (2D) frustrated Heisenberg systems, where spins order in a nonplanar way at T=0. This model, consisting of coupled trihedra (or Ising-RP3 model), encompasses Ising (chiral) degrees of freedom, spin-wave excitations, and Z2 vortices. Extensive Monte Carlo simulations show that the T=0 chiral order disappears at finite temperature in a continuous phase transition in the 2D Ising universality class, despite misleading intermediate-size effects observed at the transition. The analysis of configurations reveals that short-range spin fluctuations and Z2 vortices proliferate near the chiral domain walls, explaining the strong renormalization of the transition temperature. Chiral domain walls can themselves carry an unlocalized Z2 topological charge, and vortices are then preferentially paired with charged walls. Further, we conjecture that the anomalous size effects suggest the proximity of the present model to a tricritical point. A body of results is presented, which all support this claim: (i) first-order transitions obtained by Monte Carlo simulations on several related models, (ii) approximate mapping between the Ising-RP3 model and a dilute Ising model (exhibiting a tricritical point), and, finally, (iii) mean-field results obtained for Ising-multispin Hamiltonians, derived from the high-temperature expansion for the vector spins of the Ising-RP3 model.


[36] "Quantum Dimer Model on the triangular lattice : Semiclassical and variational approaches to vison dispersion and condensation "
Gregoire Misguich, Frederic Mila .
Phys. Rev. B 77, 134421 (2008) (pdf)
"Editors' Suggestions"

Abstract: After reviewing the concept of vison excitations in Z2 dimer liquids, we study the liquid-crystal transition of the Quantum Dimer Model on the triangular lattice by means of a semiclassical spin-wave approximation to the dispersion of visons in the context of a "soft-dimer" version of the model. This approach captures some important qualitative features of the transition: continuous nature of the transition, linear dispersion at the critical point, and \sqrt{12}x\sqrt{12} symmetry-breaking pattern. In a second part, we present a variational calculation of the vison dispersion relation at the RK point which reproduces the qualitative shape of the dispersion relation and the order of magnitude of the gap. This approach provides a simple but reliable approximation of the vison wave-functions at the RK point.


[35] "Magnetic-Field Induced Bose-Einstein Condensation of Magnons and Critical Behavior in Interacting Spin Dimer System TlCuCl3 "
Fumiko Yamada, Toshio Ono, Hidekazu Tanaka, Gregoire Misguich, Masaki Oshikawa, Toshiro Sakakibara .
J. Phys. Soc. Jpn. 77, 013701 (2008) (pdf)
"Paper of Editors' Choice"

Abstract: Magnetization measurements were performed to investigate the critical behavior of the field-induced magnetic ordering in gapped spin system TlCuCl3. The critical density of the magnons was obtained as a function of temperature and the magnon-magnon interaction constant was evaluated. The experimental phase boundary for T<5K agrees almost perfectly with the magnon BEC theory based on the Hartree-Fock approximation with realistic dispersion relations. The phase boundary can be described by the power law [HN(T)-Hc] ~ Tphi. With decreasing fitting temperature range, the critical exponent phi decreases and converges at phiBEC=3/2 predicted by the magnon BEC theory.


[34] "Magnetic susceptibility and specific heat of the spin-1/2 Heisenberg model on the kagome lattice and experimental data on ZnCu3(OH)6Cl2 "
Gregoire Misguich, Philippe Sindzingre .
Eur. Phys. J. B 59, 305 (2007) (pdf)
Abstract: We compute the magnetic susceptibility and specific heat of the spin-1/2 Heisenberg model on the kagome lattice with high-temperature expansions and exact diagonalizations. We compare the results with the experimental data on ZnCu3(OH)6Cl2 obtained by Helton et al. [Phys. Rev. Lett. 98, 107204 (2007)]. Down to kBT/J~0.2, our calculations reproduce accurately the experimental susceptibility, with an exchange interaction J~190K and a contribution of 3.7% of weakly interacting impurity spins. The comparison between our calculations of the specific heat and the experiments indicate that the low-temperature entropy (below ~20K) is smaller in ZnCu3(OH)6Cl2 than in the kagome Heisenberg model, a likely signature of other interactions in the system.


[33] "Topological Entanglement Entropy in the Quantum Dimer Model on the Triangular Lattice "
Shunsuke Furukawa, Gregoire Misguich .
Phys. Rev. B 75, 214407 (2007) (pdf)
Abstract: A characterization of topological order in terms of entanglement was proposed recently [A. Kitaev and J. Preskill, Phys. Rev. Lett. 96, 110404 (2006); M. Levin and X.-G. Wen, ibid, 110405]. It was argued that, in a topological phase, there is a universal additive constant in the entanglement entropy, called topological entanglement entropy, determined by the underlying gauge theory of topological order. In the present paper we evaluate numerically the topological entanglement entropy in the ground states of a quantum dimer model on the triangular lattice, which is known to have a Z2 topological ordered phase. We examine the two original constructions to measure the topological entanglement entropy, and we observe that they both approach the value expected for Z2 topological order, in the large-area limit. We also consider the entanglement entropy on a ``zigzag'' topologically non-trivial area and propose to use it as a more accurate way to measure topological entanglement entropies.


[32] "Detecting spontaneous symmetry breaking in finite-size spectra of frustrated quantum antiferromagnets "
Gregoire Misguich, Philippe Sindzingre .
J. Phys.: Condens. Matter 19, 145202 (2007). (pdf)
Proceedings of the International Conference "Highly Frustrated Magnets", Osaka (Japan), August 2006.

Abstract: Exact diagonalization is a powerful numerical technique to analyze static and dynamical quantities in quantum many-body lattice models. It provides unbiased information concerning quantum numbers, energies and wave-functions of the low-energy eigenstates for almost any kind of microscopic model. The information about energies and quantum numbers is particularly useful to detect possible spontaneous symmetry breaking at T=0. We review some of the advances in the field of frustrated quantum magnets which have been possible thanks to detailed symmetry analysis of exact diagonalizations spectra. New results concerning the kagome and star lattice Heisenberg antiferromagnets are presented.


[31] "Classical dimers with aligning interactions on the square lattice "
Fabien Alet, Yacine Ikhlef, Jesper Lykke Jacobsen, Gregoire Misguich, Vincent Pasquier .
Phys. Rev. E 74, 041124 (2006) (pdf)
Abstract: We present a detailed study of a model of close-packed dimers on the square lattice with an interaction between nearest-neighbor dimers. The interaction favors parallel alignment of dimers, resulting in a low-temperature crystalline phase. With large-scale Monte Carlo and Transfer Matrix calculations, we show that the crystal melts through a Kosterlitz-Thouless phase transition to give rise to a high-temperature critical phase, with algebraic decays of correlations functions with exponents that vary continuously with the temperature. We give a theoretical interpretation of these results by mapping the model to a Coulomb gas, whose coupling constant and associated exponents are calculated numerically with high precision. Introducing monomers is a marginal perturbation at the Kosterlitz-Thouless transition and gives rise to another critical line. We study this line numerically, showing that it is in the Ashkin-Teller universality class, and terminates in a tricritical point at finite temperature and monomer fugacity. In the course of this work, we also derive analytic results relevant to the non-interacting case of dimer coverings, including a Bethe Ansatz (at the free fermion point) analysis, a detailed discussion of the effective height model and a free field analysis of height fluctuations.


[30] "Reduced density matrices and topological order in a quantum dimer model "
Shunsuke Furukawa, Gregoire Misguich, Masaki Oshikawa .
J. Phys.: Condens. Matter 19, 145212 (2007)
Proceedings of the International Conference "Highly Frustrated Magnets", Osaka (Japan), August 2006.

Abstract: Resonating valence bond (RVB) liquids in two dimensions are believed to exhibit topological order and to admit no local order parameter of any kind. This is a defining property of "liquids" but it has been explicitly confirmed only in a few exactly solvable models. In this paper, we investigate the quantum dimer model on the triangular lattice. It possesses an RVB-type liquid phase, however, for which the absence of the local order parameter has not been proved. We examine the question numerically with a measure based on reduced density matrices. We find a scaling of the measure which strongly supports the absence of any local order parameter.


[29] "Unconventional continuous phase transition in a three dimensional dimer model "
Fabien Alet, Gregoire Misguich, Vincent Pasquier, Roderich Moessner, Jesper Lykke Jacobsen .
Phys. Rev. Lett. 97, 030403 (2006) (pdf)
Abstract: Phase transitions occupy a central role in physics, due both to their experimental ubiquity and their fundamental conceptual importance. The explanation of universality at phase transitions was the great success of the theory formulated by Ginzburg and Landau, and extended through the renormalization group by Wilson. However, recent theoretical suggestions have challenged this point of view in certain situations. In this Letter we report the first large-scale simulations of a three-dimensional model proposed to be a candidate for requiring a description beyond the Landau-Ginzburg-Wilson framework: we study the phase transition from the dimer crystal to the Coulomb phase in the cubic dimer model. Our numerical results strongly indicate that the transition is continuous and is compatible with a tricritical universality class, at variance with previous proposals.


[28] "Local spin spirals in the Neel phase of La2-xSrxCuO4 "
Andreas Luscher, Gregoire Misguich, Alexander I. Milstein and Oleg P. Sushkov .
Phys. Rev. B 73, 085122 (2006) (pdf)
Abstract: Experimental observations of lightly doped La2-xSrxCuO4 x<0.02, revealed remarkable magnetic properties such as the incommensurate noncollinear ordering (additional to the Neel ordering) and a tremendous doping dependence of the uniform longitudinal susceptibility. We show that the spiral solution of the t-t'-t''-J model obtained by taking into account the Coulomb trapping of holes by Sr ions describes these puzzling data perfectly well. Our solution firstly explains why the incommensurate structure is directed along the orthorhombic b-axis, and secondly allows a numerical calculation of the positions and shapes of the incommensurate neutron scattering peaks. Thirdly, we calculate the doping dependence of the spin-wave gap, and lastly, we study the longitudinal magnetic susceptibility and show that its doping dependence is due to the noncollinearity of the spin spiral.


[27] "Systematic derivation of order parameters through reduced density matrices "
Shunsuke Furukawa, Gregoire Misguich and Masaki Oshikawa .
Phys. Rev. Lett. 96, 047211 (2006) (pdf)
Abstract: A systematic method for determining order parameters for quantum many-body systems on lattices is developed by utilizing reduced density matrices. This method allows one to extract the order parameter directly from the wave functions of the degenerate ground states without aid of empirical knowledge, and thus opens a way to explore unknown exotic orders. The applicability of this method is demonstrated numerically or rigorously in models which are considered to exhibit dimer, scalar chiral, and topological orders.


[26] "Detection of Exotic Order Parameters of Quantum Antiferromagnets through Reduced Density Matrices "
Shunsuke Furukawa, Gregoire Misguich and Masaki Oshikawa .
Progress of Theoretical Physics Supplement 159, 143 (2005)


[25] "Interacting classical dimers on the square lattice "
F. Alet, J. L. Jacobsen, G. Misguich, V. Pasquier, F. Mila, and M. Troyer .
Phys. Rev. Lett. 94, 235702 (2005) (pdf)
Abstract: We study a model of close-packed dimers on the square lattice with a nearest neighbor interaction between parallel dimers. This model corresponds to the classical limit of quantum dimer models [D. S. Rokhsar and S. A. Kivelson, Phys. Rev. Lett. 61, 2376 (1988)]. By means of Monte Carlo and transfer matrix calculations, we show that this system undergoes a Kosterlitz-Thouless transition separating a low temperature ordered phase where dimers are aligned in columns from a high temperature critical phase with continuously varying exponents. This is understood by constructing the corresponding Coulomb gas, whose coupling constant is computed numerically. We also discuss doped models and implications on the finite-temperature phase diagram of quantum dimer models.


[24] "Quantum dimer model with Z2 liquid ground-state: interpolation between cylinder and disk topologies and toy model for a topological quantum-bit "
G. Misguich, V. Pasquier, F. Mila and C. Lhuillier .
Phys. Rev. B 71, 184424 (2005) (pdf)
Abstract: We consider a quantum dimer model (QDM) on the kagome lattice which was introduced recently [Phys. Rev. Lett. 89, 137202 (2002)]. It realizes a Z2 liquid phase and its spectrum was obtained exactly. It displays a topological degeneracy when the lattice has a non-trivial geometry (cylinder, torus, etc). We discuss and solve two extensions of the model where perturbations along lines are introduced: first the introduction of a potential energy term repelling (or attracting) the dimers along a line is added, second a perturbation allowing to create, move or destroy monomers. For each of these perturbations we show that there exists a critical value above which, in the thermodynamic limit, the degeneracy of the ground-state is lifted from 2 (on a cylinder) to 1. In both cases the exact value of the gap between the first two levels is obtained by a mapping to an Ising chain in transverse field. This model provides an example of solvable Hamiltonian for a topological quantum bit where the two perturbations act as a diagonal and a transverse operator in the two-dimensional subspace. We discuss how crossing the transitions may be used in the manipulation of the quantum bit to optimize simultaneously the frequency of operation and the losses due to decoherence.


[23] "Specific heat of the S=1/2 Heisenberg model on the kagome lattice: high-temperature series expansion analysis "
G. Misguich and B. Bernu .
Phys. Rev. B 71, 014417 (2005) (pdf)
Abstract: We compute specific heat of the antiferromagnetic spin-1/2 Heisenberg model on the kagome lattice. We use a recently introduced technique to analyze high-temperature series expansion based on the knowledge of high-temperature series expansions, the total entropy of the system and the low-temperature expected behavior of the specific heat as well as the ground-state energy. In the case of kagome-lattice antiferromagnet, this method predicts a low-temperature peak at T/J<0.1.


[22] "Bose-Einstein Condensation of Magnons in TlCuCl3: Phase diagram and specific heat from a self-consistent Hartee-Fock calculation with a realistic dispersion relation "
G. Misguich and M. Oshikawa .
J. Phys. Soc. Jpn. 73, 3429 (2004) (pdf)
Abstract: We extend the self-consistent Hartree-Fock-Popov calculations by Nikuni et al. [Phys. Rev. Lett. 84, 5868 (2000)] concerning the Bose-Eistein condensation of magnons in TlCuCl3 to include a realistic dispersion of the excitations. The result for the critical field as a function of temperature behaves as Hc(T)-Hc(0)~T3/2 below 2K but deviates from this simple power-law at higher temperature and is in very good agreement with the experimental results. The specific heat is computed as a function of temperature for different values of the magnetic field. It shows a lambda-like shape at the transition and is in good qualitative agreement with the results of Oosawa et al. [Phys. Rev. B 63, 134416 (2001)].


[21] "Soliton binding and low-lying singlets in frustrated odd-legged S=1/2 spin tubes "
A. Luscher, R. M. Noack, G. Misguich, V. N. Kotov and F. Mila .
Phys. Rev. B 70, 060405(R) (2004) (pdf)
Abstract: Motivated by the intriguing properties of the vanadium spin tube Na2V3O7, we show that an effective spin-chirality model similar to that of standard Heisenberg odd-legged S=1/2 spin tubes can be derived for frustrated inter-ring couplings, but with a spin-chirality coupling constant alpha that can be arbitrarily small. Using density matrix renormalization group and analytical arguments, we show that, while spontaneous dimerization is always present, solitons become bound into low-lying singlets as alpha is reduced. Experimental implications for strongly frustrated tubes are discussed.


[20] "Cyclic exchange, isolated states, and spinon deconfinement in an XXZ Heisenberg model on the checkerboard lattice "
N. Shannon, G. Misguich, and K. Penc .
Phys. Rev. B 69, 220403(R) (2004) (pdf)
Abstract: The antiferromagnetic Ising model on a checkerboard lattice has an ice-like ground state manifold with extensive degeneracy. and, to leading order in Jxy, deconfined spinon excitations. We explore the role of cyclic exchange arising at order Jxy2/Jz on the ice states and their associated spinon excitations. By mapping the original problem onto an equivalent quantum six-vertex model, we identify three different phases as a function of the chemical potential for flippable plaquettes.a phase with long range Néel order and confined spinon excitations, a nonmagnetic state of resonating square plaquettes, and a quasicollinear phase with gapped but deconfined spinon excitations. The relevance of the results to the square-lattice quantum dimer model is also discussed.


[19] "Interaction between static holes in a quantum dimer model on the kagome lattice "
G. Misguich, D. Serban and Vincent Pasquier .
J. Phys.: Cond. Mat. 16, 823 (2004) (pdf)
Abstract: A quantum dimer model (QDM) on the kagome lattice with an extensive ground-state entropy was recently introduced [Phys. Rev. B 67, 214413 (2003)]. The ground-state energy of this QDM in presence of one and two static holes is investigated by means of exact diagonalizations on lattices containing up to 144 kagome sites. The interaction energy between the holes (at distances up to 7 lattice spacings) is evaluated and the results show no indication of confinement at large hole separations.


[18] "Two-dimensional quantum antiferromagnets "
G. Misguich and C. Lhuillier .
Review chapter in the book ``Frustrated spin systems'', edited by H. T. Diep, World-Scientific (2005). [cond-mat/0310405]
Abstract: This review presents some theoretical advances in the field of quantum magnetism in two-dimensional systems. Among the subjects which are discussed: the spin-1/2 J1-J2 Heisenberg model on the square lattice, valence-bond crystals, large-N methods, quantum dimer models, the physics of multiple-spin exchange interactions, RVB spin liquids as well as the spin-1/2 Heisenberg model on the kagome lattice.


[17] "Ising transition driven by frustration in a 2D classical model with continuous symmetry "
C. Weber, L. Capriotti, G. Misguich, F. Becca, M. Elhajal and F. Mila .
Phys. Rev. Lett. 91, 177202 (2003) (pdf)
Abstract: We study the thermal properties of the classical antiferromagnetic Heisenberg model with both nearest (J1) and next-nearest (J2) exchange couplings on the square lattice by extensive Monte Carlo simulations. We show that, for J2/J1 > 1/2, thermal fluctuations give rise to an effective Z2 symmetry leading to a finite-temperature phase transition. We provide strong numerical evidence that this transition is in the 2D Ising universality class, and that Tc->0 with an infinite slope when J2/J1->1/2.


[16] "Determination of the exchange energies in Li2VOSiO4 from a high-temperature series analysis of the square lattice J1-J2 Heisenberg model "
G. Misguich, B. Bernu, L. Pierre .
Phys. Rev. B 68, 113409 (2003) (pdf)
Abstract: We present a high-temperature expansion (HTE) of the magnetic susceptibility and specific heat data of Melzi et al. on Li2VOSiO4 [Phys. Rev. B 64, 024409 (2001)]. The data are very well reproduced by the J1-J2 Heisenberg model on the square lattice with exchange energies J1=1.25+-0.5 K and J2=5.95+-0.2 K. The maximum of the specific heat Cvmax(Tmax) is obtained as a function J2/J1 from an improved method based on HTE.


[15] "Quantum dimer model with extensive ground-state entropy on the kagome lattice "
G. Misguich, D. Serban, V. Pasquier .
Phys. Rev. B 67, 214413 (2003) (pdf)
Abstract: We introduce a quantum dimer model on the kagome lattice with kinetic terms allowing from three to six dimers to resonate around hexagons. Unlike the models studied previously, the different resonance loops appear with different signs (given by the parity of the number of dimers involved). These signs naturally appear when performing the lowest-order overlap expansion (Rokhsar and Kivelson 1988) of the Heisenberg model. We demonstrate that the quantum dimer model has an extensive zero-temperature entropy and has very short-range dimer-dimer correlations. We discuss the possible relevance of this kind of quantum dimer liquid to the physics of the spin-(1/2) Heisenberg model on the kagome lattice.


[14] "Quantum dimer model on the kagome lattice: solvable dimer liquid, and Ising gauge theory "
G. Misguich, D. Serban, V. Pasquier .
Phys. Rev. Lett. 89, 137202 (2002) (pdf)
Abstract: We introduce quantum dimer models on lattices made of corner-sharing triangles. These lattices includes the kagome lattice and can be defined in arbitrary geometry. They realize fully disordered and gapped dimer-liquid phase with topological degeneracy and deconfined fractional excitations, as well as solid phases. Using geometrical properties of the lattice, several results are obtained exactly, including the full spectrum of a dimer-liquid. These models offer a very natural - and maybe the simplest possible - framework to illustrate general concepts such as fractionalization, topological order and relation to Z2 gauge theories.


[13] "Degeneracy of the ground-state of antiferromagnetic spin-1/2 Hamiltonians "
G. Misguich, C. Lhuillier, M. Mambrini, P. Sindzingre .
Eur. Phys. J. B. 26, 167 (2002) (pdf)
Abstract: In the first part of this paper, the extension of the Lieb-Schultz-Mattis theorem to dimensions larger than one is discussed. A counter example to the original formulation of Lieb-Schultz-Mattis and Affleck is exhibited and a more precise statement is formulated. The degeneracy of the ground-state in symmetry breaking phases with long-range order is analyzed. The second and third parts of the paper concern resonating valence-bond (RVB) spin liquids. In these phases the relationship between various authors approaches: Laughlin-Oshikawa, Sutherland, Rokhsar and Kivelson, Read and Chakraborty and the Lieb-Schultz-Mattis-Affleck proposal is studied. The deep physical relation between the degeneracy property and the absence of stiffness is explained and illustrated numerically. A new conjecture is formed concerning the absolute absence of sensitivity of the spin liquid ground-states to any twist of the boundary conditions (thermodynamic limit). In the third part of the paper the relations between the quantum numbers of the degenerate multiplets of the spin liquid phases are obtained exactly. Their relationship with a topological property of the wave functions of the low lying levels of this spin liquid phase is emphasized. In spite of the degeneracy of the ground-state, we explain why these phases cannot exhibit spontaneous symmetry breaking.


[12] "Frustrated quantum magnets "
C. Lhuillier and G. Misguich .
cond-mat/0109146
Contribution to the lecture notes of the Cargese summer school on "Trends in high magnetic field science" (may 2001). Published in Lecture Notes in Physics (Springer Series) Vol 595. "High Magnetic Fields Applications in Condensed Matter Physics and Spectroscopy" (C. Berthier, L. P. Levy and G. Martinez Eds.).

Abstract: In these lectures we sketch a rapid survey of recent theoretical advances in the study of frustrated quantum magnets with a special emphasis on two dimensional magnets.


[11] "Magnetization plateaus of SrCu2(BO3)2 from a Chern-Simons theory "
G. Misguich, T. Jolicoeur, S. M. Girvin .
Phys. Rev. Lett. 87, 097203 (2001) (pdf)
Abstract: The antiferromagnetic Heisenberg model on the frustrated Shastry-Sutherland lattice is studied by a mapping onto spinless fermions carrying one quantum of statistical flux. Using a mean-field approximation these fermions populate the bands of a generalized Hofstadter problem. Their filling leads to the magnetization curve. For SrCu2(BO3)2 we reproduce plateaus at 1/3 and 1/4 of the saturation moment and predict a new one at 1/2. Gaussian fluctuations of the gauge field are shown to be massive at these plateau values.


[10] "Magnetization process from Chern-Simons theory and its application to SrCu2(BO3)2 "
Th. Jolicoeur, G. Misguich and S. M. Girvin .
Progr. Theor. Phys. Supp. 145, 76 (2002)
Proceedings of the 16th Nishinomiya-Yukawa Memorial Symposium, Nishinomiya, Japan, Nov. 2001

Abstract: In two-dimensional systems, it is possible transmute bosons into fermions by use of a Chern-Simons gauge field. Such a mapping is used to compute magnetization processes of two-dimensional magnets. The calculation of the magnetization curve then involves the structure of the Hofstadter problem for the lattice under consideration. Certain features of the Hofstadter butterfly are shown to imply the appearance of magnetization plateaus. While not always successfull, this approach leads to interesting results when applied to the 2D AF magnet SrCu2(BO3)2.


[9] "Specific heat and high-temperature series of lattice models: interpolation scheme and examples on quantum spin systems in one and two dimensions "
B. Bernu, G. Misguich .
Phys. Rev. B 63, 134409 (2001) (pdf)
Abstract: We have developed a new method for evaluating the specific heat of lattice spin systems. It is based on the knowledge of high-temperature series expansions, the total entropy of the system and the low-temperature expected behavior of the specific heat as well as the ground-state energy. By the choice of an appropriate variable (entropy as a function of energy), a stable interpolation scheme between low and high temperature is performed. Contrary to previous methods, the constraint that the total entropy is log(2S+1) for a spin S on each site is automatically satisfied. We present some applications to quantum spin models on one- and two- dimensional lattices. Remarkably, in most cases, a good accuracy is obtained down to zero temperature.


[8] "From Néel long-range order to spin-liquids in the multiple-spin exchange model "
W. LiMing, G. Misguich, P. Sindzingre and C. Lhuillier .
Phys. Rev. B 62, 6372 (2000) (pdf)
Abstract: The phase diagram of the multiple-spin exchange model on the triangular lattice is studied using exact diagonalizations. The two-spin (J2) and four-spin (J4) exchanges have been taken into account for 12, 16, 19, 21, 24, and 27 site samples in the parameter region J4=0-0.25 (for a fixed J2=1). It is found that the three-sublattice Néel ordered state built up by the pure two-spin exchange can be destroyed by the four-spin exchange, forming a spin-liquid state. The different data suggest that the phase diagram in this range of parameters exhibits two phases. The pure J2 phase is a three-sublattice Néel ordered phase, a small J4 drives it into a spin-liquid state with a spin gap filled of a large number of singlets. This spin-liquid phase is not of the same generic kind as the phase studied by Misguich et al. [Phys. Rev. B 60, 1064 (1999)]. It is observed on the finite-size samples that the Spin Liquid phase, as the Neel ordered phase, exhibits a magnetization plateau at m=1/3, and for J4>0.15 a second plateau at m=1/2. These two plateaus are associated respectively to the semi-classical orderings uud and uuud.


[7] "Magneto-thermodynamics of the spin-1/2 Kagome antiferromagnet "
P. Sindzingre, G. Misguich, C. Lhuillier, B. Bernu, L. Pierre, C. Waldtmann and H. U. Everts .
Phys. Rev. Lett. 84, 2953 (2000) (pdf)
Abstract: In this paper, we use a new hybrid method to compute the thermodynamic behavior of the spin-1/2 Kagome antiferromagnet under the influence of a large external magnetic field. We find a T2 low-temperature behavior and a very low sensitivity of the specific heat to a strong external magnetic field. We display clear evidence that this low temperature magneto-thermal effect is associated to the existence of low-lying fluctuating singlets, but also that the whole picture (T2 behavior of Cv and thermally activated spin susceptibility) implies contribution of both non magnetic and magnetic excitations. Comparison with experiments is made.


[6] "Modèle d'échange multiple sur le réseau triangulaire: Liquide de spins quantiques en deux dimensions et magnétisme des films d'3He solide "
G. Misguich and C. Lhuillier(supervisor) .
Thèse de doctorat de l'Université Paris-6 (June 1999) (pdf)
Abstract:

English. The multiple-spin exchange model is an effective description of the magnetic properties of quasilocalized fermions. We study this model for spins-1/2 on a triangular lattice and include exchanges involving 2, 3, 4, 5 and 6 particles. This hamiltonian is now recognized as relevant to the description of the nuclear magnetism of solid 3He films adsorbed on graphite. Our analysis is based on exact diagonalizations of finite size systems up to 36 sites. In a large parameter range, finite size effects, structures of spectra and correlation functions lead to the conclusion that quantum fluctuations destroy magnetic long-range order at zero temperature. The ground state is characterized by a finite correlation length; it is a spin-liquid with gapped magnetic excitations. We compute the heat capacity and find that the low-temperature entropy is significant, in agreement with experimental data. We investigate the response to an external field, and find a magnetization plateau at M/Msat=1/2. We discuss the conditions for such a plateau to appear and compare them to the better understood situations of one-dimensional systems and of classical spins. The largest sample we studied (36 sites) has a nearly fourfold degenerate ground state. This degeneracy turns out to be incompatible with a spontaneous symmetry breaking but leads us to a topological interpretation. We propose a short-ranged ``resonating valence-bond'' (RVB) picture of the ground state wave-function and discuss the possible relation to the Haldane phase or ``valence-bond solid'' states. The multiple-spin exchange model on the triangular lattice seems to be one of the very first examples of two-dimensional spin-1/2 model without any broken symmetry at zero temperature.

French. L'échange multiple d'écrit de manière effective les propriétés magnétiques d'un système de fermions quasiment localisés. Nous considérons ce modèle pour des spins-1/2 sur le réseau triangulaire avec des processus à 2, 3, 4, 5 et 6 particules. Cet hamiltonien est aujourd'hui reconnu comme étant un bon candidat pour décrire le magnétisme nucléaire des films d'3He solide adsorbés sur du graphite. Nous l'étudions par diagonalisations exactes sur des échantillons jusqu'à 36 sites. Dans un large domaine de paramètres, l'analyse des effets de taille finie sur les énergies propres, la structure des spectres et les fonctions de corrélation amènent à conclure que les fluctuations quantiques détruisent l'ordre magnétique à température nulle. L'état fondamental est caractérisé par une longueur de corrélation finie, c'est un liquide de spins où les excitations magnétiques possèdent un gap. Nous calculons la chaleur spécifique et trouvons une entropie importante à basse température, en accord avec les mesures expérimentales. La réponse à un champ extérieur révèle un plateau d'aimantation à M/Msat=1/2. Nous discutons les conditions d'apparition d'un tel plateau et les comparons avec les situations, mieux comprises, de la dimension un ainsi que celle de spins classiques. Pour le plus grand système étudié (36 sites), le fondamental possède une quasi-dégénérescence quatre. Cette dégénérescence ne s'explique pas par une brisure spontanée de symétrie mais elle conduit à une interprétation topologique. Nous suggérons une image de ``resonating valence-bond'' (RVB) à courte portée pour la fonction d'onde du fondamental et discutons du lien éventuel avec la phase de Haldane et les états de type ``valence-bond solid''. Le modèle d'échange multiple sur le réseau triangulaire semble un des tous premiers exemples d'hamiltonien bidimensionnel de spins-1/2 dont le fondamental ne brise aucune de symérie à température nulle.


[5] "Spin-Liquid phase of the Multiple-Spin Exchange Hamiltonian on the Triangular Lattice "
G. Misguich, C. Lhuillier, B. Bernu and C. Waldtmann .
Phys. Rev. B 60, 1064 (1999) (pdf)
Abstract: We performed an exact diagonalization study of the spin liquid phase of the Multiple-Spin Exchange model on the triangular lattice. It is characterized by no Néel Long Range Order (NLRO), short-ranged magnetic correlations and a spin gap. We found no LRO in any local order parameter we investigated (chiral, dimer,...). The probable asymptotic ground state degeneracy is discussed. We argue that it could be of topological origin and that the system is probably not a chiral spin liquid. A possible relation to the Affleck-Kennedy-Lieb-Tasaki (AKLT) phase is discussed.


[4] "Spin Liquid in the Multiple-Spin Exchange Model on the triangular lattice: 3He on graphite "
G. Misguich, B. Bernu, C. Lhuillier and C. Waldtmann .
Phys. Rev. Lett. 81, 1098, (1998) (pdf)
Abstract: Using exact diagonalizations, we investigate the T = 0 phase diagram of the multiple-spin exchange (MSE) model on the triangular lattice, we find a transition separating a ferromagnetic phase from a nonmagnetic gapped spin liquid phase. Systems far enough from the ferromagnetic transition have a metamagnetic behavior with magnetization plateaus at M/Msat = 0 and 1/2 . The MSE has been proposed to describe solid 3He films adsorbed onto graphite, thus we compute the MSE heat capacity for parameters in the low density range of the 2nd layer and find a double-peak structure.


[3] "The Multiple-Spin Exchange Phase Diagram on the Triangular Lattice: Schwinger-Boson analysis "
G. Misguich, B. Bernu and C. Lhuillier .
J. of Low Temp. Phys. vol. 110, 327 (1998)
Proceedings of the QFS'97 conference

Abstract: We present the classical phase diagram of a multiple-spin exchange hamiltonian involving up to five-particle exchange. Schwinger-boson (mean field theory) calculations confirm the classical picture of competing ferromagnetic and antiferromagnetic phases, and suggest that the frustration induced by four-particle exchange might destroy long range order.


[2] "Geometrically Frustrated Quantum Antiferromagnets and Spin Liquids "
C. Lhuillier, B. Bernu and G. Misguich .
Int. Journal of Mod. Phys. B. vol.13 Nos. 5 & 6, 687 (1999)
Proceedings of the 9th International Conference on recent progress in Many Body Theories, Sydney, August 1997

Abstract: We briefly review experimental and theoretical results related to the problem of long range magnetic order in geometrically frustrated 2-dimensional quantum antiferromagnets. We show that 2-dimensional 3He at low coverage is a good candidate as a Spin-Liquid. We underline that sophisticated numerical studies of the spectra of such systems point at least to two different kinds of Spin-Liquids.


[1] "Alkali suboxides as weaker binding substrates for helium "
J. Dupont-Roc, G. Misguich and L. Girlanda .
Czech. J. Phys. 46, 419 (1996)
Abstract: Suboxides of heavy alkali metals are known for their particularly low work function. This property should make the surface of those materials less binding for helium than that of pure metals. A semi-quantitative assessment of their wetting properties for liquid helium is proposed. Preparation of such surfaces has been undertaken for rubidium suboxides. The wetting properties obtained for liquid helium will be reported.


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