Transport and Temperature 1: Exact spectrum and resistivity for the one-dimensional infinite-$U$ Hubbard model

TL;DR

This paper derives an exact energy spectrum and analytical expression for charge transport in the 1D infinite-U Hubbard model, revealing linear-in-temperature resistivity behavior relevant to strange metals.

Contribution

It provides an explicit, beyond Bethe ansatz, analytical solution for the spectrum and Drude weight in the model, offering insights into strange-metal transport phenomena.

Findings

Exact energy spectrum constructed for the model.

Derived a closed-form expression for the charge Drude weight.

Identified linear-in-T correction to the Drude weight leading to resistivity behavior.

Abstract

Understanding charge transport in strongly correlated systems remains a central challenge in condensed matter physics, particularly in light of the ubiquitous linear-in-$T$ resistivity observed in strange metals across many platforms from bulk cuprates to twisted bilayer graphene. Here, we investigate charge transport in the one-dimensional Hubbard model in the infinite-interaction limit. Focusing on the dilute limit with a fixed number of doped holes, we first construct the exact \emph{and explicit - i.e. beyond Bethe ansatz} energy spectrum and then derive a closed-form analytical expression for the charge Drude weight at arbitrary temperatures. We further analyze the low-temperature scaling and identify a linear-in-$T$ correction to the Drude weight. Upon regularizing the singular Drude contribution to the DC conductivity, we find that this behavior corresponds to an effective linear-in-$T$ resistivity, which may provide analytical insight into the emergence of strange-metal transport in two-dimensional strongly correlated systems.