Finite-temperature charge transport in the one-dimensional Hubbard model

TL;DR

This paper investigates charge transport in the one-dimensional Hubbard model at finite temperature, revealing the vanishing of the Drude weight with system size and analyzing the effects of mass imbalance on conductivity and diffusion.

Contribution

It applies dynamical quantum typicality to study larger systems than before, providing new insights into charge transport and the effects of mass imbalance in the Hubbard model.

Findings

Charge Drude weight vanishes with power law as system size increases.

Finite dc conductivity suggests diffusive transport despite finite-size effects.

Conductivity decreases exponentially with mass imbalance, with finite values for certain ratios.

Abstract

We study the charge conductivity of the one-dimensional repulsive Hubbard model at finite temperature using the method of dynamical quantum typicality, focusing at half filling. This numerical approach allows us to obtain current autocorrelation functions from systems with as many as 18 sites, way beyond the range of standard exact diagonalization. Our data clearly suggest that the charge Drude weight vanishes with a power law as a function of system size. The low-frequency dependence of the conductivity is consistent with a finite dc value and thus with diffusion, despite large finite-size effects. Furthermore, we consider the mass-imbalanced Hubbard model for which the charge Drude weight decays exponentially with system size, as expected for a non-integrable model. We analyze the conductivity and diffusion constant as a function of the mass imbalance and we observe that the conductivity of the lighter component decreases exponentially fast with the mass-imbalance ratio. While in the extreme limit of immobile heavy particles, the Falicov-Kimball model, there is an effective Anderson-localization mechanism leading to a vanishing conductivity of the lighter species, we resolve finite conductivities for an inverse mass ratio of $\eta \gtrsim 0.25$.