Nonequivalence of ensembles for long-range quantum spin systems in optical lattices

TL;DR

This paper investigates the nonequivalence of microcanonical and canonical ensembles in long-range quantum spin systems, revealing that their thermodynamics can differ significantly, especially in optical lattice experiments with anisotropic interactions.

Contribution

It provides an analytical calculation of microcanonical entropy for a long-range quantum Heisenberg model and demonstrates ensemble nonequivalence due to anisotropy.

Findings

Microcanonical and canonical ensembles are nonequivalent for certain anisotropy parameters.

The microcanonical entropy shape indicates similarity to the Curie-Weiss Ising model in canonical thermodynamics.

The results are relevant for understanding long-range quantum spin systems in optical lattices.

Abstract

Motivated by the anisotropic long-range nature of the interactions between cold dipolar atoms or molecules in an optical lattice, we study the anisotropic quantum Heisenberg model with Curie-Weiss-type long-range interactions. Absence of a heat bath in optical lattice experiments suggests a study of this model within the microcanonical ensemble. The microcanonical entropy is calculated analytically, and nonequivalence of microcanonical and canonical ensembles is found for a range of anisotropy parameters. 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 differs. Qualitatively, the observed features of nonequivalent ensembles are expected to be relevant for long-range quantum spin systems realized in optical lattice experiments.