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

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 $5{\pi }^2/36$.

arXiv comment14 pages, 6 figures

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• Charge fluctuations, hydrodynamics and transport in the square-lattice Hubbard model
• Thermal conductivity and heat diffusion in the two-dimensional Hubbard model
• Strange metal behavior from incoherent carriers scattered by local moments
• Towards numerically exact computation of conductivity in the thermodynamic limit of interacting lattice models
• Strange metallicity in an antiferromagnetic quantum critical model: A sign-problem-free quantum Monte-Carlo study
• Conductivity of lattice bosons at high temperatures
• Hot band sound