A coordinate Bethe ansatz approach to the calculation of equilibrium and nonequilibrium correlations of the one-dimensional Bose gas

TL;DR

This paper employs the coordinate Bethe ansatz to precisely compute equilibrium and nonequilibrium correlations in the one-dimensional Lieb-Liniger Bose gas, revealing nonthermal behaviors post-quench and dependence on interaction strength.

Contribution

It introduces an exact Bethe ansatz-based method to analyze both static and dynamic correlations in the Lieb-Liniger model, including nonequilibrium quenches from different initial states.

Findings

Correlation functions depend on interaction strength and system size.

Time-averaged correlations after quenches are nonthermal.

Distinct initial states lead to different nonthermal steady states.

Abstract

We use the coordinate Bethe ansatz to exactly calculate matrix elements between eigenstates of the Lieb-Liniger model of one-dimensional bosons interacting via a two-body delta-potential. We investigate the static correlation functions of the zero-temperature ground state and their dependence on interaction strength, and analyze the effects of system size in the crossover from few-body to mesoscopic regimes for up to seven particles. We also obtain time-dependent nonequilibrium correlation functions for five particles following quenches of the interaction strength from two distinct initial states. One quench is from the non-interacting ground state and the other from a correlated ground state near the strongly interacting Tonks-Girardeau regime. The final interaction strength and conserved energy are chosen to be the same for both quenches. The integrability of the model highly constrains its dynamics, and we demonstrate that the time-averaged correlation functions following quenches from these two distinct initial conditions are both nonthermal and moreover distinct from one another.