Optical Conductivity of the Two-Dimensional Hubbard Model

TL;DR

This paper investigates the charge dynamics of the two-dimensional Hubbard model, revealing incoherent behavior near the Mott transition and providing insights into its universality class through optical conductivity and Drude weight analysis.

Contribution

It presents Lanczos diagonalization results for optical conductivity and Drude weight, highlighting differences between 1D and 2D behaviors and characterizing the Mott transition's universality class.

Findings

Large incoherence below the upper-Hubbard band in 2D

Suppressed Drude weight near the Mott transition in 2D

Consistent results with quantum Monte Carlo indicating a z=4 universality class

Abstract

Charge dynamics of the two-dimensional Hubbard model is investigated. Lancz$\ddot{\rm o}$s-diagonalization results for the optical conductivity and the Drude weight of this model are presented. Near the Mott transition, large incoherence below the upper-Hubbard band is obtained together with a remarkably suppressed Drude weight in two dimensions while the clearly coherent character is shown in one dimension. The two-dimensional results are consistent with previous results from quantum Monte Carlo calculations indicating that the Mott transition in this two-dimensional model belongs to the universality class characterized by the dynamical exponent of $z=4$.