Quantum Mechanical Limitations to Spin Diffusion in the Unitary Fermi Gas

We compute spin transport in the unitary Fermi gas using the strong-coupling Luttinger-Ward theory. In the quantum degenerate regime the spin diffusivity attains a minimum value of Dₛ1.3/m approaching the quantum limit of diffusion for a particle of mass m. Conversely, the spin drag rate reaches a maximum value of Γsd1.2kBTF/ in terms of the Fermi temperature TF. The frequency-dependent spin conductivity σₛ(ω) exhibits a broad Drude peak, with spectral weight transferred to a universal high-frequency tail σₛ(ω→∞)=1/2C/3π(mω)3/2 proportional to the Tan contact density C. For the spin susceptibility χₛ(T) we find no downturn in the normal phase.