Competing Orders in One-Dimensional Half-Integer Fermionic Cold Atoms: A Conformal Field Theory Approach
arXiv:0711.4731 · doi:10.1016/j.nuclphysb.2007.12.034
Abstract
The physical properties of arbitrary half-integer spins F = N - 1/2 fermionic cold atoms loaded into a one-dimensional optical lattice are investigated by means of a conformal field theory approach. We show that for attractive interactions two different superfluid phases emerge for F \ge 3/2: A BCS pairing phase, and a molecular superfluid phase which is formed from bound-states made of 2N fermions. In the low-energy approach, the competition between these instabilities and charge-density waves is described in terms of Z_N parafermionic degrees of freedom. The quantum phase transition for F=3/2,5/2 is universal and shown to belong to the Ising and three-state Potts universality classes respectively. For a filling of one atom per site, a Mott transition occurs and the nature of the possible Mott-insulating phases are determined.
35 pages, 3 figures, final version to appear in Nucl. Phys. B
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