Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model

Abstract

The ground and excited states of a one-dimensional (1D) spin-1/2 Fermi gas (SFG) with both attractive zero-range odd-wave interactions and repulsive zero-range even-wave interactions are mapped exactly to a 1D Lieb-Liniger-Heisenberg (LLH) model with delta-function repulsions depending on isotropic Heisenberg spin-spin interactions, such that the complete SFG and LLH energy spectra are identical. The ground state in the ferromagnetic phase is given exactly by the Lieb-Liniger (LL) Bethe ansatz, and that in the antiferromagnetic phase by a variational method combining Bethe ansatz solutions of the LL and 1D Heisenberg models. There are excitation branches corresponding to LL type I and II phonons and spin waves, the latter behaving quadratically for small wave number in the ferromagnetic phase and linearly in the antiferromagnetic phase.

arXiv comment4 pages, 2 figures, revtex4. To be submitted to Phys. Rev. Lett

References in corpus (15)

• Atomic Scattering in Presence of an External Confinement and a Gas of Impenetrable Bosons
• Transition from a strongly interacting 1D superfluid to a Mott insulator
• Regimes of quantum degeneracy in trapped 1D gases
• Controlled Collapse of a Bose-Einstein Condensate
• Atom-Atom Scattering Under Cylindrical Harmonic Confinement: Numerical and Analytical Studies of the Confinement Induced Resonance
• Fermion-Boson Duality of One-dimensional Quantum Particles with Generalized Contact Interaction
• Realizing Discontinuous Wave Functions with Renormalized Short-Range Potentials
• Tuning the interactions of spin-polarized fermions using quasi-one-dimensional confinement
• Spin waves in a one-dimensional spinor Bose gas
• Theory of spinor Fermi and Bose gases in tight atom waveguides
• Effective interactions, Fermi-Bose duality, and ground states of ultracold atomic vapors in tight de Broglie waveguides
• Two component interacting bosons: 1-d exact results
• Exact results of the ground state and excitation properties of a two-component interacting Bose system
• Bosonization, Pairing, and Superconductivity of the Fermionic Tonks-Girardeau Gas
• Pairing of a harmonically trapped fermionic Tonks-Girardeau gas

Cited by in corpus (19)

• An Interaction-Driven Many-Particle Quantum Heat Engine: Universal Behavior
• High-fidelity rapid ground-state loading of an ultracold gas into an optical lattice
• Ground-state properties of one-dimensional anyon gases
• Junctions of anyonic Luttinger wires
• Ground-state properties of hard-core anyons in one-dimensional optical lattices
• Dynamical properties of hard-core anyons in one-dimensional optical lattices
• One-particle density matrix and momentum distribution function of one-dimensional anyon gases
• Entanglement properties and moment distributions of a system of hard-core anyons on a ring
• CONAN -- the cruncher of local exchange coefficients for strongly interacting confined systems in one dimension
• One-dimensional anyons with competing $\delta$-function and derivative $\delta$-function potentials
• One-body reduced density matrix of trapped impenetrable anyons in one dimension
• Off-diagonal correlations in one-dimensional anyonic models: A replica approach
• Universal off-diagonal long-range order behaviour for a trapped Tonks-Girardeau gas
• Ramsey interferometry with a two-level Tonks-Girardeau gas
• Unitary $p$-wave Fermi gas in one dimension
• Stability of spinor Fermi gases in tight waveguides
• Pairing, off-diagonal long-range order, and quantum phase transition in strongly attracting ultracold Bose gas mixtures in tight waveguides
• Generalized Bose-Fermi mapping and strong coupling ansatz wavefunction for one dimensional strongly interacting spinor quantum gases
• Dualities for anyons