Phys. Rev. Lett. 97, 210401 (2006) [4 pages]
Ground and Excited States of Spinor Fermi Gases in Tight Waveguides and the Lieb-Liniger-Heisenberg Model
Abstract
References (28)
Citing Articles
M. D. GirardeauCollege of Optical Sciences, University of Arizona, Tucson, Arizona 85721, USA
Received 5 October 2006; published 21 November 2006
The ground and excited states of a one-dimensional (1D) spin- 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.
©2006 The American Physical Society
| URL: |
http://link.aps.org/doi/10.1103/PhysRevLett.97.210401
|
| DOI: |
10.1103/PhysRevLett.97.210401 |
| PACS: |
05.30.Fk;
03.75.Mn
|
REFERENCES (28)
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