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arXiv:0809.1475 · Physical Review B

Photoinduced Tomonaga-Luttinger-like liquid in a Mott insulator

Takashi Oka, Hideo Aoki

Published Dec 31, 2008• 25 citations
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Abstract

Photoinduced metallic states in a Mott insulator are studied for the half-filled one-dimensional Hubbard model with the time-dependent density-matrix renormalization group. An irradiation of strong ac fields is found to create, in the nonequilibrium steady state, a linear dispersion in the optical spectrum (current-current correlation) reminiscent of the Tomonaga-Luttinger liquid for the doped Mott insulator in equilibrium. The spin spectrum in nonequilibrium retains the des Cloizeaux--Pearson mode with the spin velocity differing from the charge velocity. The mechanism of the photocarrier doping, along with the renormalization in the charge velocity, is analyzed in terms of an effective Dirac model.

DOI
10.1103/physrevb.78.241104

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Photoinduced metallic states in a Mott insulator are studied for the half-filled one-dimensional Hubbard model with the time-dependent density-matrix renormalization group. An irradiation of strong ac fields is found to create, in the nonequilibrium steady state, a linear dispersion in the optical spectrum (current-current correlation) reminiscent of the Tomonaga-Luttinger liquid for the doped Mott insulator in equilibrium. The spin spectrum in nonequilibrium retains the des Cloizeaux--Pearson mode with the spin velocity differing from the charge velocity. The mechanism of the photocarrier doping, along with the renormalization in the charge velocity, is analyzed in terms of an effective Dirac model.
We theoretically study the properties of the photo-carriers created in a one-dimensional Mott insulator subject to strong AC electric fields. The time-dependent density matrix renormalization group method is used to calculate the nonlinear optical conductivity, for which a metallic, gapless mode is found to emerge. The mode has linear dispersion with a charge velocity that differs from the free electron velocity, which indicates that the photo-doped carriers behave collectively as in the Tomonaga-Luttinger liquid.
Nonlinear transport in the one dimensional Hubbard model at half-filling under a finite bias voltage is investigated by the adaptive time-dependent density matrix renormalization group method. For repulsive on-site interaction, dielectric breakdown of the Mott insulating ground state to a current-carrying nonequilibrium steady state is clearly observed when the voltage exceeds the charge gap. It is found that by increasing the voltage further the current-voltage characteristics are scaled only by the charge gap and the scaling curve exhibits almost linear dependence on the voltage whose slope is suppressed by the electron correlation. In the case of attractive interaction the linear conductance is the perfect one 2e2/h2e^2/h2e2/h which agrees with the prediction by the Luttinger liquid theory.
Utilizing the exact diagonalization method, we investigate the one-dimensional Peierls-Hubbard model at quarter filling, where it manifests as an antiferromagnetic Mott insulator in units of dimers. By increasing the on-site Coulomb repulsion UUU, we observe a significant suppression of the Drude peak, based on a nonequilibrium linear-response theory capable of capturing the zero-frequency (Drude) weight of the optical conductivity under periodic boundary conditions. However, after the ultrafast photoirradiation of this model with large UUU, we detect a distinct enhancement of the Drude peak, signifying the onset of a photoinduced insulator-metal transition. Comparing these dynamics with the half-filled Hubbard model and a noninteracting spinless half-filled Su-Schrieffer-Heeger model (corresponding to the quarter-filled Peierls-Hubbard model with infinite UUU), we propose a mechanism for the photoinduced metallic state: The empty-occupied and double-occupied dimers serve as the photoinduced charge carriers, akin to the holons and doublons in the Hubbard model.
We study the interplay between an on-site Hubbard repulsion and quasiperiodic potential in one-dimensional fermion chains using the density matrix renormalization group. We find that, at half filling, the quasiperiodic potential can destroy the Mott gap, leading to a metallic Luttinger liquid phase between the gapped Mott insulator at strong repulsion and the localized gapless Aubry-Andr\'e insulator at strong quasiperiodic potential. Away from half filling, the metallic phase of the interacting model persists to larger critical strengths of the potential than in the noninteracting case, suggesting interaction-stabilized delocalization at finite doping. We characterize the Luttinger liquid through its charge and spin correlations, structure factors, and entanglement entropy.
The spectrum of charge excitations, Im N ( q , ω), has been evaluated near the Mott transition in the one-dimensional Hubbard model with a particular value of the Coulomb interaction. The present theory based on a continuum limit describes the smooth change between the Tomonaga-Luttinger liquid state with a q -linear mode and the Mott insulator with a charge gap, by considering Umklapp scattering. The charge susceptibility is seen to diverge proportional to the inverse of the doping rate as the Mott insulator state is approached, in agreement with Bethe-ansatz result. It is shown that the q region where the renormalization group theory and conformal field theory are valid becomes vanishingly small as the transition is approached.
We use time-evolution techniques for (infinite) matrix product states to calculate, directly in the thermodynamic limit, the time-dependent photoemission spectra and dynamic structure factors of the half-filled Hubbard chain after pulse irradiation.These quantities exhibit clear signatures of the photoinduced phase transition from insulator to metal that occurs because of the formation of so-called η pairs.In addition, the spin dynamic structure factor loses spectral weight in the whole momentum space, reflecting the suppression of antiferromagnetic correlations due to the buildup of η-pairing states.The numerical method demonstrated in this work can be readily applied to other one-dimensional models driven out of equilibrium by optical pumping.