Can Hubbard model resist electric current?

TL;DR

This paper demonstrates that the two-dimensional Hubbard model cannot sustain a steady electric current at finite temperature, contradicting recent claims, and clarifies its conductive behavior and limitations.

Contribution

It provides a perturbative proof that the Hubbard model cannot support a steady current under a uniform electric field at finite temperature, challenging previous simulation results.

Findings

Hubbard model is perfectly conducting in linear response

No steady state current can be supported at finite temperature

The model exhibits Bloch oscillations under finite electric field

Abstract

It is claimed by a recent quantum Monte Carlo simulation that the linear-in-temperature DC resistivity observed in the high-$T_{c}$ cuprate superconductors can be reproduced in the pure two dimensional Hubbard model\cite{Huang}. Here we show perturbatively that such a translational invariant electronic model can not support a steady state current in the presence of a uniform electric field at any finite temperature. Instead, the Hubbard model is perfectly conducting in the linear response regime and will undergo Bloch oscillation at finite electric field for any finite temperature. Nevertheless, the quantum Monte Carlo simulation can provide us the key information on the temperature dependence of the Drude weight, a quantity of central importance in the holographic description of the transport properties of the strange metal phase.