Sine-Gordon model at finite temperature: the method of random surfaces

TL;DR

This paper introduces a non-perturbative method based on random surfaces to analyze the finite-temperature sine-Gordon model, providing accurate free energy and operator expectation values in the gapped phase.

Contribution

The authors extend the method of random surfaces to finite-temperature quantum field theory, offering a new approach for strongly interacting 1D systems and validating it against known results.

Findings

Excellent agreement with existing methods at moderate temperatures

Accurate computation of free energy and one-point functions

Potential applicability to broader strongly interacting systems

Abstract

We study the sine-Gordon quantum field theory at finite temperature by generalizing the method of random surfaces to compute the free energy and one-point functions of exponential operators non-perturbatively. Focusing on the gapped phase of the sine-Gordon model, we demonstrate the method's accuracy by comparing our results to the predictions of other methods and to exact results in the thermodynamic limit. We find excellent agreement between the method of random surfaces and other approaches when the temperature is not too small with respect to the mass gap. Extending the method to more general problems in strongly interacting one-dimensional quantum systems is discussed.