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

摘要

We review the recently introduced thermodynamic form factors for pairs ofparticle-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 usedfor analytic computations of dynamical correlation functions. We derive a newrepresentation for the form factors and we discuss some aspects of theirstructure. We rigorously show that in the small momentum limit (orequivalently, on hydrodynamic scales) a single particle-hole excitation fullysaturates the spectral sum and we also discuss the contribution from twoparticle-hole pairs. Finally we show that thermodynamic form factors can bealso used to study the ground state correlations and to derive the edgeexponents.