On the Equivalence of the KMS Condition and the Variational Principle for Quantum Lattice Systems with Mean-Field Interactions

TL;DR

This paper extends the equivalence between the KMS condition and the variational principle to quantum lattice systems with mean-field interactions, broadening understanding of equilibrium states in long-range interacting models.

Contribution

It generalizes Araki's results to include models with mean-field interactions, using recent advances in free energy minimization and infinite volume dynamics.

Findings

Established the equivalence for a large class of mean-field models.

Connected the KMS condition with the variational principle in long-range interaction systems.

Extended the theoretical framework for quantum lattice systems with mean-field interactions.

Abstract

We extend Araki's well-known results on the equivalence of the KMS condition and the variational principle for equilibrium states of quantum lattice systems with short-range interactions, to a large class of models possibly containing mean-field interactions (representing an extreme form of long-range interactions). This result is reminiscent of van Hemmen's work on equilibrium states for mean-field models. The extension was made possible by our recent outcomes on states minimizing the free energy density of mean-field models on the lattice, as well as on the infinite volume dynamics for such models.