Restoring integrability in one-dimensional quantum gases by two-particle correlations

TL;DR

This paper demonstrates that in one-dimensional quantum gases, strong pairwise quantum correlations suppress three-body interactions, thereby preserving integrability even when local three-body elastic interactions are present.

Contribution

It reveals that quantum correlations, not the freeze-out of two-body collisions, are key to maintaining integrability in 1D quantum systems with three-body interactions.

Findings

Three-particle scattering is suppressed by a factor of (k/c)^{12} at small relative momentum.

Quantum correlations prevent thermalization caused by three-body interactions.

Strong correlations restore integrability in the Lieb-Liniger model despite three-body interactions.

Abstract

We show that thermalization and the breakdown of integrability in the one dimensional Lieb-Liniger model caused by local three-body elastic interactions is suppressed by pairwise quantum correlations when approaching the strongly correlated regime. If the relative momentum $k$ is small compared to the two-body coupling constant $c$ the three-particle scattering state is suppressed by a factor of $(k/c)^{12}$. This demonstrates that in one dimensional quantum systems it is not the freeze-out of two body collisions but the strong quantum correlations which ensures integrability.