Bounds on Correlation Functions of Quantum Rotators

TL;DR

This paper derives bounds on correlation functions of quantum rotators in one dimension, explores the system's partition function, and discusses the potential for a Kosterlitz-Thouless phase transition within the Villain approximation.

Contribution

It introduces a McBryan-Spencer bound for quantum rotators and analyzes the phase structure, including the possibility of a Kosterlitz-Thouless transition.

Findings

Established a lower bound on charge correlation functions.

Derived the partition function in the gas representation.

Discussed conditions for a Kosterlitz-Thouless phase.

Abstract

We derive a McBryan-Spencer bound to the correlation function of a one-dimensional array of quantum rotators in the Villain approximation of the cosine interaction. We obtain the partition function of the system in the gas representation and establish a lower bound on the external charge correlation function. We also discuss the possible existence of a Kosterlitz-Thouless phase for the quantum rotator in the Villain approximation.