# Modèle d'échange multiple sur le réseau triangulaire : liquide de spins quantiques en deux dimensions et magnétisme des films d'3He solide

Abstract : 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.
Mots-clés :

https://tel.archives-ouvertes.fr/tel-00001115
Contributor : Marc Gingold <>
Submitted on : Wednesday, February 20, 2002 - 4:54:14 PM
Last modification on : Friday, May 29, 2020 - 4:01:16 PM
Document(s) archivé(s) le : Tuesday, September 11, 2012 - 4:50:14 PM

### Identifiers

• HAL Id : tel-00001115, version 1

### Citation

Grégoire Misguich. Modèle d'échange multiple sur le réseau triangulaire : liquide de spins quantiques en deux dimensions et magnétisme des films d'3He solide. Matière Condensée [cond-mat]. Université Pierre et Marie Curie - Paris VI, 1999. Français. ⟨tel-00001115⟩

Record views