Some Properties of Correlations of Quantum Lattice Systems in Thermal Equilibrium

TL;DR

This paper presents simplified proofs of the uniqueness and decay of correlations in quantum lattice systems at high temperatures, introduces new quantum correlation inequalities, and extends classical decay results to quantum models with continuous symmetries.

Contribution

It provides new simplified proofs, introduces novel quantum correlation inequalities, and extends classical decay results to quantum systems with continuous symmetries.

Findings

Uniqueness of the thermodynamic limit of KMS states at high temperatures

Decay of equilibrium correlations in quantum lattice systems

New quantum correlation inequalities for Heisenberg models

Abstract

Simple proofs of uniqueness of the thermodynamic limit of KMS states and of the decay of equilibrium correlations are presented for a large class of quantum lattice systems at high temperatures. New quantum correlation inequalities for general Heisenberg models are described. Finally, a simplified derivation of a general result on power-law decay of correlations in 2D quantum lattice systems with continuous symmetries is given, extending results of Mc Bryan and Spencer for the 2D classical XY model.