Non-Fermi-Liquid Fixed Point for an Imbalanced Gas of Fermions in 1+ϵ Dimensions

We consider a gas of two species of fermions with population imbalance. Using the renormalization group in d = 1 + ϵ spatial dimensions, we show that for spinless fermions and 2 > ϵ > 0 a fixed point appears at finite attractive coupling where the quasiparticle residue vanishes, and identify this with the transition to Larkin-Ovchinnikov-Fulde-Ferrell order (inhomogeneous superconductivity). When the two species of fermions also carry spin degrees of freedom we find a fixed point indicating a transition to spin density wave order