Spectrum of elementary excitations in Galilean-invariant integrable models

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.

5 pages

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Cited by in corpus (6)

• The Casimir-like effect in a one-dimensional Bose gas
• Conjectures about the ground-state energy of the Lieb-Liniger model at weak repulsion
• Exact Results for the Boundary Energy of One-Dimensional Bosons
• Exact Results for the Moments of the Rapidity Distribution in Galilean-Invariant Integrable Models
• Method of difference-differential equations for some Bethe ansatz solvable models
• Local Properties of the Rapidity Distribution in the Lieb-Liniger Model