High-temperature transport in the Hubbard Model

We examine the general behavior of the frequency and momentum dependent single-particle scattering rate and the transport coefficients, of many-body systems in the high-temperature limit. We find that the single-particle scattering rate always saturates in temperature, while the transport coefficients always decay like $\frac{1}{T}$, where $T$ is the temperature. A consequence of this is a resistivity which is ubiquitously linear in $T$ at high temperatures. For the Hubbard model, by using the high-temperature series, we are able to calculate the first few moments of the single particle scattering rate $\Sigma(\vec{k},\omega)$ and the conductivity $\sigma(\vec{k},\omega)$ in the high-temperature regime in $d$ spatial dimensions. Further in the case of $d\to \infty$, we are able to calculate a large number of moments using symbolic computation. We make a direct comparison between these moments and those obtained through Dynamical Mean Field Theory (DMFT). Finally, we use the moments to reconstruct the $\omega$-dependent optical conductivity $\sigma(\omega) = \lim_{k\to0} \sigma(\vec{k},\omega)$ in the high-temperature regime.