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

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.

Figures (2)

• Figure 1: Normalized Drude weight $D(T)/D(0)$ as a function of temperature $T$ for (a) fixed density of holes $\delta = n_h/N = 1/4$ and (b) a single doped hole. In panel (b), the numerical Drude weight rapidly converges to the analytical prediction as the system size increases. In panel (a), a clearly distinct scaling behavior is observed. By fitting the data to the form $a + b T^{c}$, we find that the extracted exponent $c$ is larger than $1$ and approaches $2$ as the system size increases.
• Figure 2: Resistivity $\rho(T)$ as a function of temperature $T$, with the overall factor $N\eta/2$ removed. Left panel: $T \in [0,10]$. In the high-temperature regime, the slope approaches $1$. Right panel: $T \in [0,0.2]$. In the low-temperature regime, the slope approaches $1/4$.