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

M. D. Girardeau
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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.

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M. D. Girardeau. 2006-09-30. Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. https://doi.org/10.1103/physrevlett.97.210401

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