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Multiple-spin exchange model on the trinagular lattice

The subjet of my Ph. D. thesis was a study of a multiple-spin exchange model defined for spin-1/2 on a triangular lattice. This model is relevant to describe the nuclear magnetism of solid helium-3 films.

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/M_sat=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.