Exact Drude weight for the one-dimensional Hubbard model at finite temperatures

TL;DR

This paper derives an exact formula for the Drude weight in the one-dimensional Hubbard model at finite temperatures using Bethe ansatz, distinguishing metallic and Mott-insulating states through low-temperature analysis.

Contribution

It provides the first exact finite-temperature Drude weight formula for the 1D Hubbard model based on Bethe ansatz and analyzes its behavior at different fillings.

Findings

Exact Drude weight formula derived from Bethe ansatz.

Low-temperature expansions differentiate metallic and Mott-insulating states.

Results clarify transport properties at finite temperatures.

Abstract

The Drude weight for the one-dimensional Hubbard model is investigated at finite temperatures by using the Bethe ansatz solution. Evaluating finite-size corrections to the thermodynamic Bethe ansatz equations, we obtain the formula for the Drude weight as the response of the system to an external gauge potential. We perform low-temperature expansions of the Drude weight in the case of half-filling as well as away from half-filling, which clearly distinguish the Mott-insulating state from the metallic state.