High-temperature series expansions for quantum spin models
I am working with
B. Bernu
and L. Pierre
on
high-temperature series expansion techniques applied to
lattice spin models.
We devised a simple method to extrapolate the
high-temperature series expansion of the specific
heat cv(T) to zero temperature for
lattice models. It applies to spin models without
finite-temperature phase transition such as
low-dimensional quantum magnets. For many such models
the following data are available: 1) Ground-state and
infinite temperature energies. 2) Leading terms of
the high-temperature expansion of the free energy. 3)
Total entropy per spin, which is just log(2S+1). 4)
Qualitative low-temperature behavior of
cv(T). We combined these informations into
a procedure to estimate cv(T). To do so,
we perform a two-point Pad\'e interpolation on the
entropy as a function of the energy. Going back to
cv(T), we get a result which, in addition
to matching the high-temperature expansion, exactly
satisfies two sum rules imposed by the knowledge of
the ground-state energy and the total entropy: int
cv(T)dT=E(T=infinity)-E(T=0) and int
cv(T)/TdT=log(2S+1). We have illustrated
this method on several systems (spin chains and many
two-dimensional spin-1/2 Heisenberg models). These
sum rules turn out to constrain cv(T) so
that, unlike other standard approaches, accurate
results can be obtained (relative error of the order
of a few percent) down to zero
temperature.
As applications of the method above, we studied some
finite-temperature thermodynamic properties of two
(antiferromagnetic) Heisenberg spin-1/2 models in two
dimensions with the help of high-temperature series:
on the kagome lattice and on the square lattice with
first and second-neighbor couplings (so called
J1-J2 model). The kagome model
is one of the simplest quantum spin models which
physics is so poorly understood. Our results give
quantitative informations about the weight and
location of the low-temperature peak in the specific
heat of the kagome quantum antiferromagnet. In the
second model we analyzed experimental magnetic
susceptibility data for the compound
Li2VOSiO4 and provided accurate
estimates of the couplings J1 and
J2 this quasi two-dimensional vanadium
oxide.
References:
- B. Bernu, G. Misguich
-
Phys. Rev. B
63, 134409 (2001).
- G. Misguich, B. Bernu and L. Pierre
-
Phys. Rev. B
68, 113409 (2003).
- G. Misguich and B. Bernu
-
Phys. Rev. B
71, 014417 (2005).
[or cond-mat/0407277].
- NEW: Online calculation of specific-heat curves (experimental!)
-
www.myworksonline.com
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