Optical conductivity of a Hubbard ring with an impurity

TL;DR

This paper studies how an impurity affects the optical conductivity of a Hubbard ring, revealing impurity-induced spectral shifts and in-gap states through exact diagonalization, with implications for understanding finite metallic and insulating systems.

Contribution

It provides a detailed analysis of impurity effects on optical conductivity in Hubbard rings, including spectral shifts and impurity states, using exact diagonalization methods.

Findings

Impurity shifts the Drude peak to finite frequencies proportional to impurity strength.

Impurity induces in-gap states in the Mott insulating phase.

Impurity effects depend on the interaction strength and boundary conditions.

Abstract

We investigate the optical conductivity of a Hubbard ring in presence of an impurity by means of exact diagonalization using the Lanczos algorithm. We concentrate thereby on the first excited, open shell state, i.e. on twisted boundary conditions. In the metallic phase a substantial part of the spectral weight lies in the Drude peak, $\sigma(\omega) = D\delta(\omega)+ \sigma_{\rm reg}$. In the non-interacting system, the Drude peak can be visualized in our calculations at $\omega = 0$ even for finite chain lengths. Adding the impurity, the main peak is shifted to finite frequencies proportional to the impurity strength. The shift indicates the energy gap of the disturbed finite size system, also in the interacting system. Thus, we can pursue in the optical conductivity for finite metallic systems the energy gap. However, due to level crossing, the impurity-induced peak arises in the interacting system first when a certain impurity strength is exceeded. In the Mott insulating phase, the impurity leads to an impurity state within the gap.