Two-spinon effects on the thermal Tonks-Girardeau gas

TL;DR

This paper investigates how two-spinon excitations influence the thermal correlations in the Tonks-Girardeau gas, revealing their dominant role at low temperatures and demonstrating the effectiveness of the two-spinon approach.

Contribution

It extends the analysis of two-spinon effects from the ground state to finite temperatures in the Lieb-Liniger model, showing their dominance in the correlation function.

Findings

Two-spinon excitations dominate at low temperatures.

Adding particle-hole excitations reduces their contribution.

Numerical results show convergence of the correlation function.

Abstract

We study the effects of the two-spinon excitations on the field-field correlator of the Tonks-Girardeau gas. While these excitations have been previously examined in the ground state of the system, their role at finite temperatures remains unexplored. Here, we extend the analysis to the one-dimensional interacting Bose gas at thermal equilibrium, focusing on the one-body correlation function of the infinitely repulsive Lieb-Liniger model. We demonstrate that two-spinon excitations, characterized by two holes within the rapidity distribution, constitute the dominant contribution to the field-field correlator at low temperatures. Furthermore, we analytically show that incorporating additional particle-hole excitations diminishes their contribution, highlighting the efficacy of the two-spinon framework in capturing the essential physics of the system. Numerical evaluations of both the Fredholm determinant and the spectral sum stemming from the two-spinon program, with the addition of particle-hole excitations, reveal convergence at low temperatures.