Particle-hole pairs and density-density correlations in the Lieb-Liniger model

TL;DR

This paper reviews thermodynamic form factors for particle-hole pairs in the Lieb-Liniger model, demonstrating their use in calculating dynamical correlations and ground state properties.

Contribution

It introduces a new representation for form factors and rigorously analyzes their role in spectral sums and correlation functions in the Lieb-Liniger model.

Findings

Single particle-hole excitation saturates spectral sum at small momentum

Thermodynamic form factors can compute ground state correlations

Edge exponents can be derived from form factors

Abstract

We review the recently introduced thermodynamic form factors for pairs of particle-hole excitations on finite-entropy states in the Lieb-Liniger model. We focus on the density operator and we show how the form factors can be used for analytic computations of dynamical correlation functions. We derive a new representation for the form factors and we discuss some aspects of their structure. We rigorously show that in the small momentum limit (or equivalently, on hydrodynamic scales) a single particle-hole excitation fully saturates the spectral sum and we also discuss the contribution from two particle-hole pairs. Finally we show that thermodynamic form factors can be also used to study the ground state correlations and to derive the edge exponents.