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arXiv:1105.3145 · Physical Review B

Nonlinear doublon production in a Mott insulator: Landau-Dykhne method applied to an integrable model

Takashi Oka

Published Aug 27, 2012• 119 citations
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Abstract

Doublon-hole pair production, which takes place during dielectric breakdown in a Mott insulator subject to a strong laser or a static electric field, is studied in the one-dimensional Hubbard model. Two nonlinear effects cause the excitation, i.e., multiphoton absorption and quantum tunneling. Keldysh crossover between the two mechanisms occurs as the field strength and photon energy are changed. The calculation is done analytically by the Landau-Dykhne method in combination with the Bethe ansatz solution, and the results are compared with those of the time-dependent density matrix renormalization group. Using this method, we calculate the distribution function of the generated doublon-hole pairs and show that it drastically changes as we cross the Keldysh crossover line. After calculating the tunneling threshold for several representative one-dimensional Mott insulators, possible experimental tests of the theory are proposed, such as angle-resolved photoemission spectroscopy of the upper Hubbard band in the quantum tunneling regime. We also discuss the relationship of the present theory with a many-body extension of electron-positron pair production in nonlinear quantum electrodynamics, known as the Schwinger mechanism.

DOI
10.1103/physrevb.86.075148

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Doublon-hole pair production, which takes place during dielectric breakdown in a Mott insulator subject to a strong laser or a static electric field, is studied in the one-dimensional Hubbard model. Two nonlinear effects cause the excitation, i.e., multiphoton absorption and quantum tunneling. Keldysh crossover between the two mechanisms occurs as the field strength and photon energy are changed. The calculation is done analytically by the Landau-Dykhne method in combination with the Bethe ansatz solution, and the results are compared with those of the time-dependent density matrix renormalization group. Using this method, we calculate the distribution function of the generated doublon-hole pairs and show that it drastically changes as we cross the Keldysh crossover line. After calculating the tunneling threshold for several representative one-dimensional Mott insulators, possible experimental tests of the theory are proposed, such as angle-resolved photoemission spectroscopy of the upper Hubbard band in the quantum tunneling regime. We also discuss the relationship of the present theory with a many-body extension of electron-positron pair production in nonlinear quantum electrodynamics, known as the Schwinger mechanism.
Doublon-hole pair production which takes place during dielectric breakdown in a Mott insulator subject to a strong laser or a static electric field is studied in the one-dimensional Hubbard model. Two nonlinear effects cause the excitation, i.e., multi-photon absorption and quantum tunneling. Keldysh crossover between the two mechanisms occurs as the field strength and photon energy is changed. The calculation is done analytically by the Landau-Dykhne method in combination with the Bethe ansatz solution and the results are compared with those of the time dependent density matrix renormalization group. Using this method, we calculate distribution function of the generated doublon-hole pairs and show that it drastically changes as we cross the Keldysh crossover line. After calculating the tunneling threshold for several representative one-dimensional Mott insulators, possible experimental tests of the theory is proposed such as angle resolved photoemission spectroscopy of the upper Hubbard band in the quantum tunneling regime. We also discuss the relation of the present theory with a many-body extension of electron-positron pair production in nonlinear quantum electrodynamics known as the Schwinger mechanism.
Doublon-hole pair production which takes place during dielectric breakdown in a Mott insulator subject to a strong laser or a static electric field is studied in the one-dimensional Hubbard model. Two nonlinear effects cause the excitation, i.e., multi-photon absorption and quantum tunneling. Keldysh crossover between the two mechanisms occurs as the field strength and photon energy is changed. The calculation is done analytically by the Landau-Dykhne method in combination with the Bethe ansatz solution and the results are compared with those of the time dependent density matrix renormalization group. Using this method, we calculate distribution function of the generated doublon-hole pairs and show that it drastically changes as we cross the Keldysh crossover line. After calculating the tunneling threshold for several representative one-dimensional Mott insulators, possible experimental tests of the theory is proposed such as angle resolved photoemission spectroscopy of the upper Hubbard band in the quantum tunneling regime. We also discuss the relation of the present theory with a many-body extension of electron-positron pair production in nonlinear quantum electrodynamics known as the Schwinger mechanism.
The nonadiabatic quantum tunneling picture, which may be called the many-body Schwinger-Landau-Zener mechanism, for the dielectric breakdown of Mott insulators in strong electric fields is studied in the one-dimensional Hubbard model. The tunneling probability is calculated by a method due to Dykhne-Davis-Pechukas with an analytical continuation of the Bethe-ansatz solution for excited states to a non-Hermitian case. A remarkable agreement with the time-dependent density-matrix renormalization-group result is obtained.
Charge creation via quantum tunneling, i.e. dielectric breakdown, is one of the most fundamental and significant phenomena arising from strong light(field)-matter coupling. In this work, we conduct a systematic numerical analysis of quantum tunneling in one-dimensional Mott insulators described by the extended (UUU-VVV) Hubbard model. We discuss the applicability of the analytical formula for doublon-holon (DH) pair production, previously derived for the one-dimensional Hubbard model, which highlights the relationship between the tunneling threshold, the charge gap, and the correlation length. We test the formulas ability to predict both DH pair production and energy increase rate. Using tensor-network-based approaches, we demonstrate that the formula provides accurate predictions in the absence of excitonic states facilitated by the nearest-neighbor interaction VVV. However, when excitonic states emerge, the formula more accurately describes the rate of energy increase than the DH pair creation rate and in both cases gets improved by incorporating the exciton energy as the effective gap.
The breakdown of a Mott-insulator when subjected to intense laser fields is characterized by the formation of doublon-hole pairs. This breakdown is furthermore evidenced by the production of high harmonics that can be experimentally measured. Here, we present an approach for extracting the doublon-hole correlation length of a Mott insulator. The method is based on a dynamical calculation of the Mott insulator’s rate of charge production in response to an applied strong-field laser pulse. We find that coupling the Mott insulator to a metal drastically increases the correlation length, in support of our recent hypothesis [ Phys. Rev. B 108 , 144434 ( 2023 ) 2469-9950 10.1103/PhysRevB.108.144434 ] that coupling to a metal enhances the charge fluctuations in the insulator. We confirm our conclusions using density matrix renormalization group (DMRG) calculations. The proposed method can be applied to experimentally measured observables, such as differential reflectivity or the high harmonic generation (HHG) spectrum to extract doublon-hole correlation length.
Using dynamical mean-field theory and the non-crossing approximation as impurity solver, we study the response of a Mott insulator to strong dc electric fields. The breakdown of the Mott insulating state is triggered by field-induced creation of doublon-hole pairs. In a previous investigation, Ref. [1], it was found that the system approaches a long-lived quasi-steady state in which the current is time-independent although the number of carriers constantly increases. Here we investigate and clarify the nature of this state, which exists only because thermalization is slow in the Hubbard model at strong coupling. The current is time-independent because doublons and holes have an infinite temperature distribution. Evidence for this fact is obtained from spectral functions and by comparing the electric current with the field-induced doublon-hole creation rate. Implications to real experiments, in systems with energy dissipation, are discussed.