Comparative study of one-dimensional Bose and Fermi gases with contact interactions from the viewpoint of universal relations for correlation functions

Abstract

One-dimensional spinless Bose and Fermi gases with contact interactions have the close interrelation via Girardeau's Bose-Fermi mapping, leading to the correspondences in their energy spectra and thermodynamics. However, correlation functions are in general not identical between these systems. We derive in both systems the exact universal relations for correlation functions, which hold for any energy eigenstate and any statistical ensemble of the eigenstates with or without a trapping potential. These relations include the large-momentum behaviors of static structure factors and of momentum distributions as well as energy relations, which connect the sums of kinetic and interaction energies to the momentum distributions. The relations involve two- and three-body contacts, which are the integrals of local pair and triad correlations, respectively. We clarify how the relations for bosons and fermions differ and are connected with each other. In particular, we find that the three-body contact makes no contribution to the bosonic energy relation, but it plays a crucial role in the fermionic one. In addition, we compute the exact momentum distribution for any number of fermions in the unitary limit.

8 pages, no figure; published version

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Cited by in corpus (18)

• Field-theoretical aspects of one-dimensional Bose and Fermi gases with contact interactions
• Unitary $p$-wave Fermi gas in one dimension
• Emergent s-wave interactions between identical fermions in quasi-one-dimensional geometries
• Stability against three-body clustering in one-dimensional spinless p-wave fermions
• Ground-state properties of dilute spinless fermions in fractional dimensions
• Optical spin transport theory of spin-1/2 topological Fermi superfluids
• Transport in p-wave interacting Fermi gases
• Bulk viscosity of dual Bose and Fermi gases in one dimension
• Thermodynamic contacts and breathing mode physics of 1D p-wave Fermi gases in the high temperature limit
• Viscous Flow in a 1D Spin-Polarized Fermi Gas: the Role of Integrability on Viscosity
• Three-body contact for fermions. I. General relations
• Universal composite boson formation in strongly interacting one-dimensional fermionic systems
• Non-Hermitian $p$-wave superfluid and effects of the inelastic three-body loss in a one-dimensional spin-polarized Fermi gas
• Radio-Frequency Spectroscopy and the Dimensional Crossover in Interacting Spin-Polarized Fermi Gases
• Viscous Drude weight of dual Bose and Fermi gases in one dimension
• Resonance-facilitated three-channel p-wave scattering
• Bardeen-Cooper-Schrieffer State Representation and Pairing in the Fermionic Tonks-Girardeau Gas
• Universal properties and dynamical bosonization of strongly interacting one-dimensional anyons