Quantum lattice models at intermediate temperatures

TL;DR

This paper investigates quantum lattice models at intermediate temperatures, focusing on free energy, Gibbs-KMS states, and symmetry properties, revealing phase transition behaviors without symmetry breaking.

Contribution

It provides a new analysis of quantum lattice systems at intermediate temperatures, especially regarding phase transitions and symmetry considerations.

Findings

Constructed Gibbs-KMS states for specific quantum lattice models.

Identified conditions for phase transitions without symmetry breaking.

Analyzed the role of interactions in symmetry properties at intermediate temperatures.

Abstract

We analyze the free energy and construct the Gibbs-KMS states for a class of quantum lattice systems, at low temperatures and when the interactions are almost diagonal in a suitable basis. We study systems with continuous symmetry, but our results are valid for discrete symmetry breaking only. Such phase transitions occur at intermediate temperatures where the continuous symmetry is not broken, while at very low temperature continuous symmetry breaking may occur.