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Bulletin of the American Physical Society

Sub-gap optical conductivity in the Mott insulator in one-dimensional Hubbard model with randomness

Cheng-Ju Lin, Olexei I. Motrunich

Published Mar 6, 2015• 0 citations
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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.
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 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.