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arXiv:2012.15652 · Physical review. B./Physical review. B

Nonequilibrium optical response of a one-dimensional Mott insulator

Julián Rincón, Adrian E. Feiguin

Published Aug 13, 2021• 14 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physrevb.104.085122

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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.
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.
By utilizing time-dependent tensor-network algorithms in the infinite matrix-product-state representation, we theoretically investigate the pump-probe spectroscopy of the one-dimensional extended Hubbard model at half filling. Our focus lies on nonequilibrium optical conductivity and single-particle excitation spectra. In the spin-density-wave (SDW) phase, we identify an in-gap state in the nonequilibrium optical conductivity due to the formation of excitons (or doublon-holon pairs), generated by the pulse through nonlocal interactions. In the strong-coupling regime, we discern additional multiple in-gap and out-of-gap states. In the charge-density-wave (CDW) phase, we detect not only an in-gap state but also a finite Drude weight, which results from the dissolution of charge order by photoexcitation. Analyzing time-dependent single-particle excitation spectra directly in the thermodynamic limit confirms the origin of these new states in the SDW and CDW phases as the excitation of newly emerged dispersions. We illustrate that the pump-probe spectroscopy simulations in the thermodynamic limit furnish unambiguous spectral structures that allow for direct comparison with experimental results, and the integration of nonequilibrium optical conductivity and time- and angle-resolved photoemission spectroscopy provides comprehensive insights into nonequilibrium states.
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 applied a many-body Wannier functions method to theoretically calculate the excitonic optical conductivity spectrum and energy structure in a one-dimensional (1D) Mott insulator at absolute zero temperature with a large system size. Focusing on full charge fluctuations associated with holon and doublon pairs, we employ a charge model, which is interpreted as an effective model for investigating the photoexcitations of a 1D extended Hubbard model under a half-filling of the spin-charge separation. As a result, theoretical spectra with the appropriate broadenings qualitatively reproduce the recent experimental data of ET-F2TCNQ{\mathrm{F}}_{2}\mathrm{TCNQ}F2​TCNQ at 294 K with and without a modulated electric field. Regarding the excitonic energy structure, we found that the excitons, particularly for even-parity, are weakly bound by many-body effects. This is also consistent with the fitting parameters reported in a recent experiment. Thus, the theoretical method presented in this paper is useful for understanding the physical roles of the charge fluctuations in many-body excited states of a 1D Mott insulator.
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.