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 $D_s \simeq 1.3 \hbar/m$ approaching the quantum limit of diffusion for a particle of mass $m$. Conversely, the spin drag rate reaches a maximum value of $\Gamma_\sd \simeq 1.2 k_B T_F/\hbar$ in terms of the Fermi temperature $T_F$. The frequency-dependent spin conductivity $\sigma_s(\omega)$ exhibits a broad Drude peak, with spectral weight transferred to a universal high-frequency tail $\sigma_s(\omega \to\infty) = \hbar^{1/2}C/3\pi(m\omega)^{3/2}$ proportional to the Tan contact density $C$. For the spin susceptibility $\chi_s(T)$ we find no downturn in the normal phase.