Relaxation dynamics of the Lieb-Liniger gas following an interaction quench: A coordinate Bethe-ansatz analysis

TL;DR

This study examines how a one-dimensional Bose gas with contact interactions relaxes after a sudden increase in interaction strength, using coordinate Bethe-ansatz to analyze small systems and compare with thermodynamic predictions.

Contribution

It provides a detailed coordinate Bethe-ansatz analysis of the nonequilibrium relaxation dynamics of the Lieb-Liniger model after an interaction quench, including correlation functions and their asymptotic behavior.

Findings

Local second-order correlations match generalized thermodynamic Bethe-ansatz predictions.

Third-order correlations show a different power-law dependence near the Tonks-Girardeau limit.

Correlation functions evolve towards equilibrium values characterized by the diagonal ensemble.

Abstract

We investigate the relaxation dynamics of the integrable Lieb-Liniger model of contact-interacting bosons in one dimension following a sudden quench of the collisional interaction strength. The system is initially prepared in its noninteracting ground state and the interaction strength is then abruptly switched to a positive value, corresponding to repulsive interactions between the bosons. We calculate equal-time correlation functions of the nonequilibrium Bose field for small systems of up to five particles via symbolic evaluation of coordinate Bethe-ansatz expressions for operator matrix elements between Lieb-Liniger eigenstates. We characterize the relaxation of the system by comparing the time-evolving correlation functions following the quench to the equilibrium correlations predicted by the diagonal ensemble and relate the behavior of these correlations to that of the quantum fidelity between the many-body wave function and the initial state of the system. Our results for the asymptotic scaling of local second-order correlations with increasing interaction strength agree with the predictions of recent generalized thermodynamic Bethe-ansatz calculations. By contrast, third-order correlations obtained within our approach exhibit a markedly different power-law dependence on the interaction strength as the Tonks-Girardeau limit of infinitely strong interactions is approached.