Spectrum of elementary excitations in Galilean-invariant integrable models

TL;DR

This paper investigates the excitation spectrum of Galilean-invariant integrable models at all momenta, revealing it is determined by ground state properties and deriving new exact relations applicable to models like Lieb-Liniger.

Contribution

It provides the first exact relations for excitation spectra at arbitrary momenta in integrable models, linking them to ground state characteristics and the Luttinger liquid parameter.

Findings

Spectrum at any momentum is determined by ground state properties.

Derived exact relations for excitation energy coefficients.

Applied formulas to Lieb-Liniger model to obtain new results.

Abstract

The spectrum of elementary excitations in one-dimensional quantum liquids is generically linear at low momenta. It is characterized by the sound velocity that can be related to the ground state energy. Here we study the spectrum at higher momenta in Galilean invariant integrable models. Somewhat surprisingly, we show that the spectrum at arbitrary momentum is fully determined by the properties of the ground state. We find general exact relations for the coefficients of several terms in the expansion of the excitation energy at low momenta and arbitrary interaction and express them in terms of the Luttinger liquid parameter. We apply the obtained formulas to the Lieb-Liniger model and obtain several new results.