FFLO transition and quantum criticality in polarized Fermi gases
We investigate the zero-temperature transition from the polarized normal phase to the FFLO state in a two-dimensional Fermi gas by means of a diagrammatic t-matrix approach. We first show that the standard non-self-consistent theory produces an unphysical phase diagram because of a severe violation of the Luttinger theorem. Motivated by this observation, we introduce a minimal self- consistent extension that largely restores compliance with the Luttinger theorem while preserving the analytical simplicity of the original formalism. This leads to a physically consistent phase diagram over the whole interaction range. Building on this improved description, we characterize the quantum critical behavior of the FFLO transition through the quasiparticle decay rates, quasiparticle weights, momentum distributions, and the critical dynamics of both fermionic and bosonic degrees of freedom. We further compare the two- and three-dimensional systems, showing that their critical properties can be understood within a unified geometrical picture based on the nesting of the majority and minority Fermi surfaces. Finally, for the three-dimensional case, we demonstrate within the Hertz-Millis framework that vertex corrections are irrelevant, thereby placing the FFLO quantum phase transition in the mean-field universality class, in close analogy with itinerant antiferromagnets.