Universal local pair correlations of Lieb-Liniger bosons at quantum criticality

TL;DR

This paper analytically derives universal local pair correlations in the Lieb-Liniger Bose gas at quantum criticality, revealing their potential to probe quantum critical behavior and Tomonaga-Luttinger liquid physics across different regimes.

Contribution

The work provides an analytical calculation of finite temperature local pair correlations at quantum criticality using Yang-Yang thermodynamics, highlighting their universality and experimental relevance.

Findings

Universal value of $g^{(2)}(0)$ in quantum critical regime

Correlation functions connect TLL and quasi-classical regions

Thermodynamic properties derived at high temperatures

Abstract

The one-dimensional Lieb-Liniger Bose gas is a prototypical many-body system featuring universal Tomonaga-Luttinger liquid (TLL) physics and free fermion quantum criticality. We analytically calculate finite temperature local pair correlations for the strong coupling Bose gas at quantum criticality using the polylog function in the framework of the Yang-Yang thermodynamic equations. We show that the local pair correlation has the universal value $g^{(2)}(0)\approx 2 p/(n\varepsilon)$ in the quantum critical regime, the TLL phase and the quasi-classical region, where $p$ is the pressure per unit length rescaled by the interaction energy $\varepsilon=\frac{\hbar^2}{2m} c^2$ with interaction strength $c$ and linear density $n$. This suggests the possibility to test finite temperature local pair correlations for the TLL in the relativistic dispersion regime and to probe quantum criticality with the local correlations beyond the TLL phase. Furthermore, thermodynamic properties at high temperatures are obtained by both high temperature and virial expansion of the Yang-Yang thermodynamic equation.