Quantum critical transport in the unitary Fermi gas

The thermodynamic and transport properties of the unitary Fermi gas at finite temperature $T$ are governed by a quantum critical point at $T=0$ and zero density. We compute the universal shear viscosity to entropy ratio $\eta /s$ in the high-temperature quantum critical regime $T\gg \left|\mu \right|$ and find that this strongly coupled quantum fluid comes close to perfect fluidity $\eta /s=\hslash /\left(4\pi k_B\right)$. Using a controlled large-$N$ expansion, we show that already at the first nontrivial order the equation of state and the Tan contact density $C$ agree well with the most recent experimental measurements and theoretical Luttinger-Ward and bold diagrammatic Monte Carlo calculations.

Figure 1

Universal phase diagram of the unitary Fermi gas.