Viscosity and scale invariance in the unitary Fermi gas

TL;DR

This paper calculates the shear viscosity of the unitary Fermi gas above the superfluid transition, revealing scale invariance effects, the importance of vertex corrections, and a minimum in the viscosity-to-entropy ratio near the transition.

Contribution

It introduces a diagrammatic approach consistent with scale invariance to compute shear viscosity and explores its frequency dependence and relation to the Tan contact.

Findings

Shear viscosity exhibits a Drude-like peak and a high-frequency tail proportional to Tan contact.

The bulk viscosity vanishes due to scale invariance.

The shear viscosity to entropy ratio has a minimum near the superfluid transition, exceeding the string theory bound.

Abstract

We compute the shear viscosity of the unitary Fermi gas above the superfluid transition temperature, using a diagrammatic technique that starts from the exact Kubo formula. The formalism obeys a Ward identity associated with scale invariance which guarantees that the bulk viscosity vanishes identically. For the shear viscosity, vertex corrections and the associated Aslamazov-Larkin contributions are shown to be crucial to reproduce the full Boltzmann equation result in the high-temperature, low fugacity limit. The frequency dependent shear viscosity $\eta(\omega)$ exhibits a Drude-like transport peak and a power-law tail at large frequencies which is proportional to the Tan contact. The weight in the transport peak is given by the equilibrium pressure, in agreement with a sum rule due to Taylor and Randeria. Near the superfluid transition the peak width is of the order of $0.5 T_F$, thus invalidating a quasiparticle description. The ratio $\eta/s$ between the static shear viscosity and the entropy density exhibits a minimum near the superfluid transition temperature whose value is larger than the string theory bound $\hbar/(4\pi k_B)$ by a factor of about seven.