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arXiv:cond-mat/0208480 · Physical review. B, Condensed matter

Optical excitations in a one-dimensional Mott insulator

Eric Jeckelmann

Published Feb 14, 2003• 82 citations
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Abstract

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).

DOI
10.1103/physrevb.67.075106

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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.
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 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 La2CuO4{\mathrm{La}}_{2}{\mathrm{CuO}}_{4}La2​CuO4​ and Nd2CuO4{\mathrm{Nd}}_{2}{\mathrm{CuO}}_{4}Nd2​CuO4​, we obtain $\text{Re}\ensuremath{\sigma}(\ensuremath{\omega})$ comparable with experiments.
We define, compute, and analyze the nonequilibrium differential optical conductivity of the one-dimensional extended Hubbard model at half-filling after applying a pump pulse, using the time-dependent density matrix renormalization group method. The melting of the Mott insulator is accompanied by a suppression of the local magnetic moment and ensuing photogeneration of doublon-holon pairs. The differential optical conductivity reveals (i) mid-gap states related to parity-forbidden optical states and (ii) strong renormalization and hybridization of the excitonic resonance and the absorption band, yielding a Fano resonance. We offer evidence and interpret such a resonance as a signature of nonequilibrium optical excitations resembling excitonic strings, (bi)excitons, and unbound doublon-holon pairs, depending on the magnitude of the intersite Coulomb repulsion. We discuss our results in the context of pump and probe spectroscopy experiments on organic Mott insulators.
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.