Transport in the 2D Fermi-Hubbard Model: Lessons from Weak Coupling

TL;DR

This paper uses quantum kinetic theory to analyze thermoelectric transport in the 2D Fermi-Hubbard model at weak coupling, revealing persistent high-temperature behaviors and novel low-temperature phenomena, with implications for cold atom experiments.

Contribution

It provides the first detailed weak coupling analysis of thermoelectric transport in the 2D Fermi-Hubbard model, connecting theoretical predictions to experimental observations.

Findings

High-temperature resistivity behaviors persist down to T~t

Nearly T-linear resistivity at half filling due to nesting

Discovery of a low-temperature Wiedemann-Franz law with Lorenz number 5π²/36

Abstract

We use quantum kinetic theory to calculate the thermoelectric transport properties of the 2D single band Fermi-Hubbard model in the weak coupling limit. For generic filling, we find that the high-temperature limiting behaviors of the electrical ($\sim T$) and thermal ($\sim T^2$) resistivities persist down to temperatures of order the hopping matrix element $T\sim t$, 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 $5\pi^2/36$.