Operator reflection positivity inequalities and their applications to interacting quantum rotors

TL;DR

This paper extends reflection positivity inequalities to operators and applies this to demonstrate long-range order in the ground state of two-dimensional quantum rotors, advancing theoretical understanding in quantum statistical mechanics.

Contribution

It generalizes the KLS-S inequality to operators and applies it to prove long-range order in quantum rotor models.

Findings

Extended KLS-S inequality to operators

Proved long-range order in 2D quantum rotors ground state

Enhanced tools for quantum statistical mechanics

Abstract

In the Reflection Positivity theory and its application to statistical mechanical systems, certain matrix inequalities play a central role. The Dyson-Lieb-Simon and Kennedy-Lieb-Shastry-Schupp inequalities constitute prominent examples. In this paper we extend the KLS-S inequality to the case where matrices are replaced by certain operators. As an application, we prove the occurrence of the long range order in the ground state of two-dimensional quantum rotors.