Generalized Lipkin–Meshkov–Glick models of Haldane–Shastry type

Abstract

We introduce a class of generalized Lipkin–Meshkov–Glick (gLMG) models with interactions of Haldane–Shastry type. We compute 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 obtain strong numerical evidence of the Gaussian character of the level density of the latter restricted Hamiltonians, and study the distribution of the spacings of consecutive unfolded levels. We also discuss the thermodynamic behavior of a large family of and gLMG models, showing that it is qualitatively similar to that of a two-level system.