Transport properties of the one-dimensional Hubbard model at finite temperature

TL;DR

This paper investigates the finite-temperature charge and spin transport in the one-dimensional Hubbard model, revealing that it behaves as a normal conductor at finite temperatures, especially when integrability-breaking interactions are present.

Contribution

It provides the first detailed numerical analysis of charge and spin transport in the finite-temperature Hubbard model, including effects of integrability-breaking interactions.

Findings

Charge current correlation decays rapidly, indicating small or zero Drude weight.

Finite DC conductivity observed with small integrability-breaking interactions.

Conductivity diverges as temperature decreases below the gap.

Abstract

We study finite-temperature transport properties of the one-dimensional Hubbard model using the density matrix renormalization group. Our aim is two-fold: First, we compute both the charge and the spin current correlation function of the integrable model at half filling. The former decays rapidly, implying that the corresponding Drude weight is either zero or very small. Second, we calculate the optical charge conductivity sigma(omega) in presence of small integrability-breaking next-nearest neighbor interactions (the extended Hubbard model). The DC conductivity is finite and diverges as the temperature is decreased below the gap. Our results thus suggest that the half-filled, gapped Hubbard model is a normal charge conductor at finite temperatures. As a testbed for our numerics, we compute sigma(omega) for the integrable XXZ spin chain in its gapped phase.