Finite temperature single-particle Green's function in the Lieb-Liniger model

TL;DR

This paper introduces a Monte Carlo algorithm to compute the finite temperature single-particle Green's function in the Lieb-Liniger model, enabling analysis across various temperatures and interactions.

Contribution

It presents a novel Monte Carlo sampling method for evaluating the Green's function's Lehmann representation in the Lieb-Liniger model at finite temperature.

Findings

Accurately determines spectral functions across temperature and interaction ranges.

Shows excellent agreement with known results at infinite interaction strength.

Extends analysis to generalized Gibbs ensembles.

Abstract

We develop a Monte Carlo sampling algorithm to numerically evaluate the Lehmann representation for the finite temperature single-particle Green's function in the repulsive Lieb-Liniger model. This allows us to determine the spectral function in the full range of temperatures and interactions, as well as in generalized Gibbs ensembles. We test our results against known results for dynamics at infinite interaction strength and static correlators, and find excellent agreement.