Optical conductivity of the Hubbard chain away from half filling

TL;DR

This paper investigates the optical conductivity in the metallic phase of the one-dimensional Hubbard model near half filling, revealing a non-power-law onset behavior above a specific energy scale.

Contribution

It combines numerical DMRG calculations with a mobile impurity model to accurately characterize the optical conductivity near the Mott gap, highlighting non-power-law behavior.

Findings

Identification of an energy scale $E_{opt}$ for conductivity onset

Confirmation that the onset is not described by a power law

Agreement between numerical data and impurity model predictions

Abstract

We consider the optical conductivity $\sigma_1(\omega)$ in the metallic phase of the one-dimensional Hubbard model. Our results focus on the vicinity of half filling and the frequency regime around the optical gap in the Mott insulating phase. By means of a density-matrix renormalization group implementation of the correction-vector approach, $\sigma_1(\omega)$ is computed for a range of interaction strengths and dopings. We identify an energy scale $E_{\rm opt}$ above which the optical conductivity shows a rapid increase. We then use a mobile impurity model in combination with exact results to determine the behavior of $\sigma_1(\omega)$ for frequencies just above $E_{\rm opt}$ which is in agreement with our numerical data. As a main result, we find that this onset behavior is not described by a power law.