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Title: Threshold singularities in a Fermi gas with attractive potential in one dimension

Abstract

We consider the one-dimensional gas of fermions with spin S interacting via an attractive δ-function potential using the Bethe Ansatz solution. In zero magnetic field the atoms form bound states of N=2S + 1 fermions, i.e. generalized Cooper states with each atom having a different spin component. For low energy excitations the system is a Luttinger liquid and is properly described by a conformal field theory with conformal charge c=1. The linear dispersion of a Luttinger liquid is asymptotically exact in the low-energy limit where the band curvature terms in the dispersion are irrelevant. For higher energy excitations, however, the spectral function displays deviations in the neighborhood of the single-particle (hole) energy, which can be described by an effective X-ray edge type model. Using the Bethe Ansatz solution we obtain expressions for the critical exponents for the single-particle (hole) Green’s function. This model can be relevant in the context of ultracold atoms with effective total spin S confined to an elongated optical trap.

Authors:
ORCiD logo [1];  [2]
  1. Florida State University, Tallahassee, FL (United States)
  2. Ukrainian National Academy of Sciences, Kharkov (Ukraine); Max-Planck-Institut für Physik komplexer Systeme, Dresden (Germany)
Publication Date:
Research Org.:
Florida State Univ., Tallahassee, FL (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
1228398
Alternate Identifier(s):
OSTI ID: 1188312
Grant/Contract Number:  
FG02-98ER45707; 4-15-13; 0112U007569
Resource Type:
Journal Article: Published Article
Journal Name:
Nuclear Physics. B
Additional Journal Information:
Journal Volume: 892; Journal Issue: C; Journal ID: ISSN 0550-3213
Publisher:
Elsevier
Country of Publication:
United States
Language:
English
Subject:
73 NUCLEAR PHYSICS AND RADIATION PHYSICS

Citation Formats

Schlottmann, P., and Zvyagin, A. A. Threshold singularities in a Fermi gas with attractive potential in one dimension. United States: N. p., 2015. Web. doi:10.1016/j.nuclphysb.2015.01.009.
Schlottmann, P., & Zvyagin, A. A. Threshold singularities in a Fermi gas with attractive potential in one dimension. United States. doi:10.1016/j.nuclphysb.2015.01.009.
Schlottmann, P., and Zvyagin, A. A. Thu . "Threshold singularities in a Fermi gas with attractive potential in one dimension". United States. doi:10.1016/j.nuclphysb.2015.01.009.
@article{osti_1228398,
title = {Threshold singularities in a Fermi gas with attractive potential in one dimension},
author = {Schlottmann, P. and Zvyagin, A. A.},
abstractNote = {We consider the one-dimensional gas of fermions with spin S interacting via an attractive δ-function potential using the Bethe Ansatz solution. In zero magnetic field the atoms form bound states of N=2S + 1 fermions, i.e. generalized Cooper states with each atom having a different spin component. For low energy excitations the system is a Luttinger liquid and is properly described by a conformal field theory with conformal charge c=1. The linear dispersion of a Luttinger liquid is asymptotically exact in the low-energy limit where the band curvature terms in the dispersion are irrelevant. For higher energy excitations, however, the spectral function displays deviations in the neighborhood of the single-particle (hole) energy, which can be described by an effective X-ray edge type model. Using the Bethe Ansatz solution we obtain expressions for the critical exponents for the single-particle (hole) Green’s function. This model can be relevant in the context of ultracold atoms with effective total spin S confined to an elongated optical trap.},
doi = {10.1016/j.nuclphysb.2015.01.009},
journal = {Nuclear Physics. B},
number = C,
volume = 892,
place = {United States},
year = {Thu Jan 15 00:00:00 EST 2015},
month = {Thu Jan 15 00:00:00 EST 2015}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record at 10.1016/j.nuclphysb.2015.01.009

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