Correlation functions of one-dimensional bosons at low temperature

TL;DR

This paper analyzes the low-temperature, long-distance behavior of density correlations in a 1D Bose gas, confirming predictions from Luttinger liquid and conformal field theories, and linking amplitudes to critical form factors.

Contribution

It provides a rigorous derivation of the asymptotic behavior of correlation functions at low temperature using algebraic Bethe ansatz, confirming and connecting theoretical predictions.

Findings

Results agree with Luttinger liquid and conformal field theory predictions.

Amplitudes match those from critical form factors.

Validates the algebraic Bethe ansatz approach for finite temperature correlations.

Abstract

We consider the low-temperature limit of the long-distance asymptotic behavior of the finite temperature density-density correlation function in the one-dimensional Bose gas derived recently in the algebraic Bethe ansatz framework. Our results confirm the predictions based on the Luttinger liquid and conformal field theory approaches. We also demonstrate that the amplitudes arising in this asymptotic expansion at low-temperature coincide with the amplitudes associated with the so-called critical form factors.