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

P. Schlottmann, A.A. Zvyagin
2015 Nuclear Physics B  
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
more » ... 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 fatcat:ceowzzy2wzhetan4i25ovg7cli