Effective mass of elementary excitations in Galilean-invariant integrable models

TL;DR

This paper investigates low-energy excitations in one-dimensional Galilean-invariant integrable models, confirming that their spectra curvature aligns with a recent phenomenological effective mass formula, with applications to Lieb-Liniger and Calogero-Sutherland models.

Contribution

It provides a rigorous proof that the excitation spectra curvature matches the phenomenological effective mass expression in integrable models with nonsingular scattering.

Findings

Spectra curvature described by the phenomenological effective mass.

Results apply to Lieb-Liniger and Calogero-Sutherland models.

Confirmed the universality of the effective mass expression.

Abstract

We study low-energy excitations of one-dimensional Galilean-invariant models integrable by Bethe ansatz and characterized by nonsingular two-particle scattering phase shifts. We prove that the curvature of the excitation spectra is described by the recently proposed phenomenological expression for the effective mass. Our results apply to such models as the repulsive Lieb-Liniger model and the hyperbolic Calogero-Sutherland model.