Non-Fermi liquid fixed point for an imbalanced gas of fermions in $1+\epsilon$ dimensions

TL;DR

This paper investigates the phase transitions in an imbalanced fermionic gas near one dimension, revealing non-Fermi liquid fixed points associated with inhomogeneous superconductivity and spin density wave order.

Contribution

It introduces a renormalization group analysis in $1+ ext{epsilon}$ dimensions showing novel fixed points for imbalanced fermions, linking them to exotic ordered phases.

Findings

Fixed point at finite attractive coupling with vanishing quasiparticle residue

Transition to inhomogeneous superconductivity (Larkin--Ovchinnikov--Fulde--Ferrell order)

Transition to spin density wave order for spinful fermions

Abstract

We consider a gas of two species of fermions with population imbalance. Using the renormalization group in $d=1+\epsilon$ dimensions, we show that for spinless fermions and $\epsilon > 0$ 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.