Universal phase diagram and scaling functions of imbalanced Fermi gases

We discuss the phase diagram and the universal scaling functions of attractive Fermi gases at finite imbalance. The existence of a quantum multicritical point for the unitary gas at vanishing chemical potential $\mu$ and effective magnetic field $h$, first discussed by Nikoli'{c} and Sachdev, gives rise to three different phase diagrams, depending on whether the inverse scattering length $1\mathrm{/}a$ is negative, positive or zero. Within a Luttinger-Ward formalism, the phase diagram and pressure of the unitary gas is calculated as a function of the dimensionless scaling variables $T\mathrm{/}\mu$ and $h\mathrm{/}\mu$. The results indicate that beyond the Clogston-Chandrasekhar limit at $(h\mathrm{/}\mu {)}_c\simeq 1.09$, the unitary gas exhibits an inhomogeneous superfluid phase with FFLO order that can reach critical temperatures near unitarity of $\simeq 0.03T_F$.