# Generalized Lipkin-Meshkov-Glick models of Haldane-Shastry type

## TL;DR

This paper introduces a new class of generalized Lipkin-Meshkov-Glick models with Haldane-Shastry type interactions, providing exact partition functions and analyzing their spectral properties and thermodynamic behavior.

## Contribution

The authors derive closed-form partition functions for generalized LMG models with su(m) interactions of Haldane-Shastry type and analyze their spectral and thermodynamic properties.

## Key findings

- Partition functions computed exactly for these models.
- Spectral level density exhibits Gaussian distribution.
- Thermodynamic behavior resembles a two-level system.

## Abstract

We introduce a class of generalized Lipkin-Meshkov-Glick (gLMG) models with su$(m)$ interactions of Haldane-Shastry type. We have computed the partition function of these models in closed form by exactly evaluating the partition function of the restriction of a spin chain Hamiltonian of Haldane-Shastry type to subspaces with well-defined magnon numbers. As a byproduct of our analysis, we have obtained strong numerical evidence of the Gaussian character of the level density of the latter restricted Hamiltonians, and studied the distribution of the spacings of consecutive unfolded levels. We have also discussed the thermodynamic behavior of a large family of su(2) and su(3) gLMG models, showing that it is qualitatively similar to that of a two-level system.