Competing orders in one-dimensional half-integer fermionic cold atoms: A conformal field theory approach

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 ⩾ 3 / 2 : A BCS pairing phase, and a molecular superfluid phase which is formed from bound-states made of 2 N 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. In contrast, for F ⩾ 7 / 2 , the transition is non-universal. For a filling of one atom per site, a Mott transition occurs and the nature of the possible Mott-insulating phases are determined.