Simulating the real time diffusive dynamics of the 2D Fermi-Hubbard on a large lattice*

I apply the Liouvillean graph effective model of [1] to the Fermi-Hubbard model.  I first consider the regimes in which the effective model is well-justified, and find that it requires interaction strength $U \sim t$ the hopping amplitude.  I then compute the finite-wavelength effective charge diffusion coefficents and momentum relaxation rate, and compare these results to the cold-atom experiment of [2].  Finally, I compute the true long-wavelength diffusion coefficent and THING; illuminating finite-size effects in the experiment [2], and compare to the Mott-Ioffe-Regel limit.

[1] Christopher David White, "Effective dissipation rate in a Liouvillean graph picture of high-temperature quantum hydrodynamics", arXiv:2108.00019

[2] Brown et al, "Bad metallic transport in a cold atom Fermi-Hubbard system", Science 363,379, 2019