Long-distance behavior of temperature correlation functions in the one-dimensional Bose gas

TL;DR

This paper develops a Bethe ansatz-based method to analyze the long-distance asymptotic behavior of temperature-dependent density correlations in a 1D Bose gas, linking integral equations with transfer matrix results.

Contribution

It introduces a novel approach combining integral representations and Bethe ansatz techniques to derive correlation lengths at finite temperature in the 1D Bose gas.

Findings

Derived explicit formulas for correlation lengths.

Connected Bethe ansatz results with quantum transfer matrix approach.

Validated the asymptotic behavior at finite temperature.

Abstract

We describe a Bethe ansatz based method to derive, starting from a multiple integral representation, the long-distance asymptotic behavior at finite temperature of the density-density correlation function in the interacting one-dimensional Bose gas. We compute the correlation lengths in terms of solutions of non-linear integral equations of the thermodynamic Bethe ansatz type. Finally, we establish a connection between the results obtained in our approach with the correlation lengths stemming from the quantum transfer matrix method.