Density form factors of the 1D Bose gas for finite entropy states

TL;DR

This paper calculates the density form factors of the 1D Bose gas in finite entropy states, enabling the derivation of dynamic correlation functions relevant for finite temperature and non-equilibrium conditions.

Contribution

It introduces a method to compute thermodynamic limit form factors for finite entropy states in the Lieb-Liniger model using Algebraic Bethe Ansatz, advancing understanding of dynamic correlations.

Findings

Computed approximate dynamic structure factor matching known results

Established a framework for form factors in finite entropy states

Enabled analysis of non-equilibrium highly excited states

Abstract

We consider the Lieb-Liniger model for a gas of bosonic $\delta-$interacting particles. Using Algebraic Bethe Ansatz results we compute the thermodynamic limit of the form factors of the density operator between finite entropy eigenstates such as finite temperature states or generic non-equilibrium highly excited states. These form factors are crucial building blocks to obtain the thermodynamic exact dynamic correlation functions of such physically relevant states. As a proof of principle we compute an approximated dynamic structure factor by including only the simplest types of particle-hole excitations and show the agreement with known results.