Excitation spectrum of the Lieb-Liniger model

Abstract

We study the integrable model of one-dimensional bosons with contact repulsion. In the limit of weak interaction, we use the microscopic hydrodynamic theory to obtain the excitation spectrum. The statistics of quasiparticles changes with the increase of momentum. At lowest momenta good quasiparticles are fermions, while at higher momenta they are Bogoliubov bosons, in accordance with recent studies. In the limit of strong interaction, we analyze the exact solution and find exact results for the spectrum in terms of the asymptotic series. Those results undoubtedly suggest that fermionic quasiparticle excitations actually exist at all momenta for moderate and strong interaction, and also at lowest momenta for arbitrary interaction. Moreover, at strong interaction we find highly accurate analytical results for several relevant quantities of the Lieb-Liniger model.

seven pages and two figures

References in corpus (8)

• Many-Body Physics with Ultracold Gases
• Bragg spectroscopy of a strongly interacting 85Rb Bose-Einstein condensate
• The dynamical spin structure factor for the anisotropic spin-1/2 Heisenberg chain
• Fermionic Quasiparticle Representation of Tomonaga-Luttinger Hamiltonian
• Decay of fermionic quasiparticles in one-dimensional quantum liquids
• Polylogs, thermodynamics and scaling functions of one-dimensional quantum many-body systems
• Low-energy excitations of a one-dimensional Bose gas with weak contact repulsion
• Decay of Bogoliubov quasiparticles in a nonideal one-dimensional Bose gas

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