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

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.

arXiv comment10 pages, 8 figures

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• Photo-induced nonequilibrium states in Mott insulators
• A Hubbard exciton fluid in a photo-doped antiferromagnetic Mott insulator
• Glassy dynamics of the one-dimensional Mott insulator excited by a strong terahertz pulse
• Anomalous suppression of photo-induced in-gap weight in the optical conductivity of a two-leg Hubbard ladder
• Many-body effects on high-harmonic generation in Hubbard ladders
• Keldysh crossover in one-dimensional Mott insulators
• Controlling inversion and time-reversal symmetries by subcycle pulses in the one-dimensional extended Hubbard model
• Observation of excitons bound by antiferromagnetic correlations
• Optical absorption activated by an ultrashort half-cycle pulse in metallic and superconducting states of the Hubbard model
• Exciton-assisted low-energy magnetic excitations in a photoexcited Mott insulator on a square lattice
• Exciton-spin interactions in antiferromagnetic charge-transfer insulators
• Low-energy photoexcitations inside the Mott gap in doped Hubbard and t-J ladders