Exact diagonalization study of optical conductivity in two-dimensional Hubbard model

TL;DR

This study uses exact diagonalization to analyze the optical conductivity in the 2D Hubbard model on small clusters, revealing doping-dependent spectral-weight transfer and insights into carrier dynamics at strong interactions.

Contribution

It provides a systematic analysis of spectral-weight transfer and carrier properties in the 2D Hubbard model using larger clusters than previous studies.

Findings

Spectral-weight distributions are similar in 20-site and 18-site clusters.

Doping affects the transfer of spectral weight from Mott-gap to lower energies.

Drude weight and carrier number depend on electron density at strong Coulomb interaction.

Abstract

The optical conductivity \sigma(\omega) in the two-dimensional Hubbard model is examined by applying the exact diagonalization technique to small square clusters with periodic boundary conditions up to \sqrt{20} X \sqrt{20} sites. Spectral-weight distributions at half filling and their doping dependence in the 20-site cluster are found to be similar to those in a \sqrt{18} X \sqrt{18} cluster, but different from 4 X 4 results. The results for the 20-site cluster enable us to perform a systematic study of the doping dependence of the spectral-weight transfer from the region of the Mott-gap excitation to lower-energy regions. We discuss the dependence of the Drude weight and the effective carrier number on the electron density at a large on-site Coulomb interaction.