Density-matrix renormalization group study of optical conductivity of the Mott insulator for two-dimensional clusters

TL;DR

This study uses the density-matrix renormalization group to analyze the optical conductivity of the two-dimensional Hubbard model, revealing excitonic peaks and their dependence on magnetic effects, with implications for understanding Mott insulators.

Contribution

First application of time-dependent density-matrix renormalization group to compute optical conductivity of 2D Hubbard model, identifying excitonic features and their magnetic origin.

Findings

Excitonic peaks observed at the Mott-gap edge in 2D and ladder systems.

No clear gap between excitonic peak and continuum in 2D lattice.

Spectral broadening due to electron-phonon interactions aligns results with experiments.

Abstract

The real part of optical conductivity $\text{Re}\sigma(\omega)$ of the Mott insulators has a large amount of information on how spin and charge degrees of freedom interact with each other. By using the time-dependent density-matrix renormalization group, we study $\text{Re}\sigma(\omega)$ of the two-dimensional Hubbard model on a square lattice at half filling. We find an excitonic peak at the Mott-gap edge of $\text{Re}\sigma(\omega)$ not only for the two-dimensional square lattice but also for two- and four-leg ladders. For the square lattice, however, we do not clearly find a gap between an excitonic peak and continuum band, which indicates that a bound state is not well defined. The emergence of an excitonic peak in $\text{Re}\sigma(\omega)$ implies the formation of a spin polaron. Examining the dependence of $\text{Re}\sigma(\omega)$ on the on-site Coulomb interaction and next-nearest neighbor hoppings, we confirm that an excitonic peak is generated from a magnetic effect. Electron scattering due to an electron-phonon interaction is expected to easily suppress an excitonic peak since spectral width of an excitonic peak is very narrow. Introducing a large broadening in $\text{Re}\sigma(\omega)$ by modeling the electron-phonon coupling present in La$_{2}$CuO$_{4}$ and Nd$_{2}$CuO$_{4}$, we obtain $\text{Re}\sigma(\omega)$ comparable with experiments.