Transport in the two-dimensional Fermi-Hubbard model: Lessons from weak coupling

We use quantum kinetic theory to calculate the thermoelectric transport properties of the two-dimensional single-band Fermi-Hubbard model in the weak coupling limit. For generic filling, we find that the high-temperature limiting behaviors of the electrical (similar to T) and thermal (similar to T-2) resistivities persist down to temperatures of order the hopping matrix element T similar to t, almost an order of magnitude below the bandwidth. At half filling, perfect nesting leads to anomalous low-temperature scattering and nearly T-linear electrical resistivity at all temperatures. We hypothesize that the T-linear resistivity observed in recent cold atom experiments is continuously connected to this weak coupling physics and suggest avenues for experimental verification. We find a number of other novel thermoelectric results, such as a low-temperature Wiedemann-Franz law with Lorenz coefficient 5 pi(2)/36.

Automated summary

The study indicates that in the Fermi-Hubbard model, for generic filling, the high-temperature limiting behaviors of electrical and thermal resistivities persist down to temperatures near the hopping matrix element T, while at half filling, anomalous low-temperature scattering results in nearly T-linear electrical resistivity. These findings suggest a continuous connection between T-linear resistivity observed in recent cold atom experiments and weak coupling physics.