Ground and Excited States of Spinor Fermi Gases in Tight Waveguides and the Lieb-Liniger-Heisenberg Model

Journal Article · Fri Nov 24 04:00:00 EST 2006 · Physical Review Letters

DOI:https://doi.org/10.1103/PHYSREVLETT.97.210401· OSTI ID:20861392

Girardeau, M D ^[1]

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1. College of Optical Sciences, University of Arizona, Tucson, Arizona 85721 (United States)

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 numbers in the ferromagnetic phase and linearly in the antiferromagnetic phase.

• OSTI ID: 20861392
• Journal Information: Physical Review Letters, Journal Name: Physical Review Letters Journal Issue: 21 Vol. 97; ISSN 0031-9007; ISSN PRLTAO
• Country of Publication: United States
• Language: English

Related Subjects

74 ATOMIC AND MOLECULAR PHYSICS
ANTIFERROMAGNETISM
DELTA FUNCTION
ENERGY SPECTRA
EXCITATION
EXCITED STATES
FERMI GAS
GROUND STATES
HEISENBERG MODEL
J-J COUPLING
MATHEMATICAL SOLUTIONS
ONE-DIMENSIONAL CALCULATIONS
PHONONS
SPIN
SPIN WAVES
VARIATIONAL METHODS
WAVEGUIDES