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arXiv:2109.06226 · Physical review. B./Physical review. B

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

Kazuya Shinjo, Yoshiki Tamaki, Shigetoshi Sota, Takami Tohyama

Published Nov 19, 2021• 15 citations
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Abstract

The real part of optical conductivity $\text{Re}\ensuremath{\sigma}(\ensuremath{\omega})$ 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 $\text{Re}\ensuremath{\sigma}(\ensuremath{\omega})$ of the two-dimensional Hubbard model on a square lattice at half filling. We find an excitonic peak at the Mott-gap edge of $\text{Re}\ensuremath{\sigma}(\ensuremath{\omega})$ 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 $\text{Re}\ensuremath{\sigma}(\ensuremath{\omega})$ implies the formation of a spin polaron. Examining the dependence of $\text{Re}\ensuremath{\sigma}(\ensuremath{\omega})$ 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 $\text{Re}\ensuremath{\sigma}(\ensuremath{\omega})$ by modeling the electron-phonon coupling present in ${\mathrm{La}}_{2}{\mathrm{CuO}}_{4}$ and ${\mathrm{Nd}}_{2}{\mathrm{CuO}}_{4}$, we obtain $\text{Re}\ensuremath{\sigma}(\ensuremath{\omega})$ comparable with experiments.

DOI
10.1103/physrevb.104.205123

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The real part of optical conductivity Re\ensuremathσ(\ensuremathω)\text{Re}\ensuremath{\sigma}(\ensuremath{\omega})Re\ensuremathσ(\ensuremathω) 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 Re\ensuremathσ(\ensuremathω)\text{Re}\ensuremath{\sigma}(\ensuremath{\omega})Re\ensuremathσ(\ensuremathω) of the two-dimensional Hubbard model on a square lattice at half filling. We find an excitonic peak at the Mott-gap edge of Re\ensuremathσ(\ensuremathω)\text{Re}\ensuremath{\sigma}(\ensuremath{\omega})Re\ensuremathσ(\ensuremathω) 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 Re\ensuremathσ(\ensuremathω)\text{Re}\ensuremath{\sigma}(\ensuremath{\omega})Re\ensuremathσ(\ensuremathω) implies the formation of a spin polaron. Examining the dependence of Re\ensuremathσ(\ensuremathω)\text{Re}\ensuremath{\sigma}(\ensuremath{\omega})Re\ensuremathσ(\ensuremathω) 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 Re\ensuremathσ(\ensuremathω)\text{Re}\ensuremath{\sigma}(\ensuremath{\omega})Re\ensuremathσ(\ensuremathω) by modeling the electron-phonon coupling present in La2CuO4{\mathrm{La}}_{2}{\mathrm{CuO}}_{4}La2​CuO4​ and Nd2CuO4{\mathrm{Nd}}_{2}{\mathrm{CuO}}_{4}Nd2​CuO4​, we obtain Re\ensuremathσ(\ensuremathω)\text{Re}\ensuremath{\sigma}(\ensuremath{\omega})Re\ensuremathσ(\ensuremathω) comparable with experiments.
The real part of optical conductivity, Reσ(ω)\text{Re}\sigma(\omega)Reσ(ω), 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 Reσ(ω)\text{Re}\sigma(\omega)Reσ(ω) of the two-dimensional Hubbard model on a square lattice at half filling. We find an excitonic peak at the Mott-gap edge of Reσ(ω)\text{Re}\sigma(\omega)Reσ(ω) 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 Reσ(ω)\text{Re}\sigma(\omega)Reσ(ω) implies the formation of a spin polaron. Examining the dependence of Reσ(ω)\text{Re}\sigma(\omega)Reσ(ω) 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 Reσ(ω)\text{Re}\sigma(\omega)Reσ(ω) by modeling the electron-phonon coupling present in La2_{2}2​CuO4_{4}4​ and Nd2_{2}2​CuO4_{4}4​, we obtain Reσ(ω)\text{Re}\sigma(\omega)Reσ(ω) comparable with experiments.
Applying newly developed dynamical density matrix renormalization group techniques at zero and finite temperatures to a Hubbard-Holstein model at half filling, we examine the optical conductivity of a typical one-dimensional Mott insulator Sr2CuO3{\text{Sr}}_{2}{\text{CuO}}_{3}Sr2​CuO3​. We find a set of parameters in the Hubbard-Holstein model, which can describe optical conductivity for both Mott-gap excitation in the high-energy region and phonon-assisted spin excitation in the low-energy region. We also find that electron-phonon interaction gives additional broadening in the temperature dependence of the Mott-gap excitation.
Abstract We numerically investigate spectroscopic properties for a two-dimensional Mott insulator described by a half-filled Hubbard model on the square lattice. Firstly, we examine the spectral shape of the optical conductivity by using time-dependent density-matrix renormalization group implemented by the Legendre polynomial expansion. We find a shape peak resembling to an excitonic peak at absorption edge, whose origin is attributable to antiferromagnetic correlation in the spin background. We next investigate momentum-dependent transient charge and spin dynamics after photoirradiation by using time-dependent Lanczos-type exact diagonalization. We find a temporal oscillation in the intensity of the dynamical spin structure factor, which exhibits an antiphase behavior between, for example, two orthogonal momentum directions parallel and perpendicular to the electric field of a pump pulse. Observing such antiphase oscillations will be a big challenge for time-resolved resonant-inelastic x-ray scattering experiments.
We employ dynamical density-matrix renormalization-group (DDMRG) and field-theory methods to determine the frequency-dependent optical conductivity in one-dimensional extended, half-filled Hubbard models. The field-theory approach is applicable to the regime of ``small'' Mott gaps which is the most difficult to access by DDMRG. For very large Mott gaps the DDMRG recovers analytical results obtained previously by means of strong-coupling techniques. We focus on exciton formation at energies below the onset of the absorption continuum. As a consequence of spin-charge separation, these Mott-Hubbard excitons are bound states of spinless, charged excitations (``holon-antiholon'' pairs). We also determine exciton binding energies and sizes. In contrast to simple band insulators, we observe that excitons exist in the Mott-insulating phase only for a sufficiently strong intersite Coulomb repulsion. Furthermore, our results show that the exciton binding energy and size are not related in a simple way to the strength of the Coulomb interaction.
The density-matrix renormalization-group (DMRG) method is used to investigate optical excitations in the Mott insulating phase of a one-dimensional extended Hubbard model. The linear optical conductivity is calculated using the dynamical DMRG method and the nature of the lowest optically excited states is investigated using a symmetrized DMRG approach. The numerical calculations agree perfectly with field-theoretical predictions for a small Mott gap and analytical results for a large Mott gap obtained with a strong-coupling analysis. It is shown that four types of optical excitations exist in this Mott insulator: pairs of unbound charge excitations, excitons, excitonic strings, and charge-density-wave (CDW) droplets. Each type of excitation dominates the low-energy optical spectrum in some region of the interaction parameter space and corresponds to distinct spectral features: a continuum starting at the Mott gap (unbound charge excitations), a single peak or several isolated peaks below the Mott gap (excitons and excitonic strings, respectively), and a continuum below the Mott gap (CDW droplets).
We employ dynamical density-matrix renormalization-group (DDMRG) and field-theory methods to determine the frequency-dependent optical conductivity in one-dimensional extended. half-filled Hubbard models. The field-theory approach is applicable to the regime of "small" Mott gaps which is the most difficult to access by DDMRG. For very large Mott gaps the DDMRG recovers analytical results obtained previously by means of strong-coupling techniques. We focus on exciton formation at energies below the onset of the absorption continuum. As a consequence of spin-charge separation, these Mott-Hubbard excitons are bound states of spinless, charged excitations ("holon-antiholon" pairs). We also determine exciton binding energies and sizes. In contrast to simple band insulators, we observe that excitons exist in the Mott-insulating phase only for a sufficiently strong intersite Coulomb repulsion. Furthermore, our results show that the exciton binding energy and size are not related in a simple way to the strength of the Coulomb interaction.