Exact correlations in the Lieb-Liniger model and detailed balance out-of-equilibrium

TL;DR

This paper derives an exact expression for the small momentum limit of the density-density correlation function in the Lieb-Liniger model, applicable to all eigenstates, and reveals a generalized detailed balance relation for dynamic structure factors.

Contribution

It provides the first exact formula for the small momentum static correlator in the Lieb-Liniger model for arbitrary eigenstates, including non-thermal states.

Findings

Exact small momentum static correlator for any eigenstate.

Generalized detailed balance relation for dynamic structure factors.

Applicable to thermal and non-thermal states.

Abstract

We study the density-density correlation function of the 1D Lieb-Liniger model and obtain an exact expression for the small momentum limit of the static correlator in the thermodynamic limit. We achieve this by summing exactly over the relevant form factors of the density operator in the small momentum limit. The result is valid for any eigenstate, including thermal and non-thermal states. We also show that the small momentum limit of the dynamic structure factors obeys a generalized detailed balance relation valid for any equilibrium state.