Nonequivalence of ensembles in the Curie-Weiss anisotropic quantum Heisenberg model

TL;DR

This paper analytically investigates the microcanonical entropy of the anisotropic quantum Heisenberg model with long-range interactions, revealing ensemble nonequivalence and similarities to the Ising model in canonical thermodynamics.

Contribution

It provides an analytical computation of the microcanonical entropy for the model, highlighting ensemble nonequivalence and the potential for experimental realization with cold gases.

Findings

Ensemble nonequivalence and partial equivalence in the model.

Indistinguishability from the Curie-Weiss Ising model in canonical thermodynamics.

Discussion on experimental realization using cold dipolar gases.

Abstract

The microcanonical entropy s(e,m) as a function of the energy e and the magnetization m is computed analytically for the anisotropic quantum Heisenberg model with Curie-Weiss-type interactions. The result shows a number of interesting properties which are peculiar to long-range interacting systems, including nonequivalence of ensembles and partial equivalence. Furthermore, from the shape of the entropy it follows that the Curie-Weiss Heisenberg model is indistinguishable from the Curie-Weiss Ising model in canonical thermodynamics, although their microcanonical thermodynamics in general differs. The possibility of experimentally realizing quantum spin models with long-range interactions in a microcanonical setting by means of cold dipolar gases in optical lattices is discussed.