Coexistence of long-range order for two observables at finite temperatures

TL;DR

This paper establishes a criterion for the simultaneous presence or absence of two long-range orders at finite temperatures in quantum lattice many-body systems, extending previous ground state results.

Contribution

It introduces a new criterion for coexistence of long-range orders at finite temperatures, generalizing earlier ground state findings and involving an inequality connecting correlation functions.

Findings

Criterion for coexistence of two long-range orders at finite T

Extension of Tian's ground state results to finite temperatures

Application to the Holstein model

Abstract

We give a criterion for the simultaneous existence or non existence of two long-range orders for two observables, at finite temperatures, for quantum lattice many body systems. Our analysis extends previous results of G.-S. Tian limited to the ground state of similar models. The proof involves an inequality of Dyson-Lieb-Simon which connects the Duhamel two-point function to the usual correlation function. An application to the special case of the Holstein model is discussed.