Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:cond-mat/0503503 · Physical Review Letters

Ground-State Decay Rate for the Zener Breakdown in Band and Mott Insulators

Takashi Oka, Hideo Aoki

Published Sep 21, 2005• 166 citations
arXivHTMLPDF

Abstract

Nonlinear transport of electrons in strong electric fields, as typified by dielectric breakdown, is reformulated in terms of the ground-state decay rate originally studied by Schwinger in nonlinear QED. We discuss the effect of electron interaction on Zener tunneling by comparing the dielectric breakdown of the band insulator and the Mott insulator, where the latter is studied by the time-dependent density-matrix renormalization group. The relation with the Berry's phase theory of polarization is also established.

DOI
10.1103/physrevlett.95.137601

Related papers

Nonequilibrium Quantum Breakdown in a Strongly Correlated Electron System

Takashi Oka, Hideo Aoki

The nonlinear transport properties of the Mott insulator are discussed with focus on the many-body Landau-Zener mechanism. After reviewing basic concepts such as the non-adiabatic geometric phase and the Schwinger mechanism, we study the decay of the insulating groundstate in strong electric fields using the time-dependent density matrix renormalization group. A short comment on the proposed mapping to the quantum walk model is added before discussing the relevance of the theory to experimental results. This article is a draft of a book chapter of the book entitled "Quantum and Semi-classical Percolation & Breakdown" (Lecture Note in Physics, Springer-Verlag), to appear 2008.

arXiv:0803.0422•Mar 4, 2008•7 citations

Dielectric breakdown in a Mott insulator: Many-body Schwinger-Landau-Zener mechanism studied with a generalized Bethe ansatz

Takashi Oka, Hideo Aoki

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.

arXiv:0903.2707•Physical Review B•Jan 14, 2010•75 citations

Dielectric Breakdown in Spin-Polarized Mott Insulator

Zala Lenarčič, Peter Prelovšek

Nonlinear response of a Mott insulator to external electric field, corresponding to dielectric breakdown phenomenon, is studied within of a one-dimensional half-filled Hubbard model. It is shown that in the limit of nearly spin-polarized insulator the decay rate of the ground state into excited holon-doublon pair can be evaluated numerically as well to high accuracy analytically. Results show that the threshold field depends on the charge gap as F(th)∝Δ(3/2). Numerical results on small systems indicate on the persistence of a similar mechanism for the breakdown for decreasing magnetization down to unpolarized system.

arXiv:1201.3817•Physical Review Letters•May 8, 2012•31 citations

Dielectric Breakdown in the 1-D Hubbard Model

Shunsuke Kirino, Kazuo Ueda

Nonequilibrium transport in the one dimensional Hubbard model at half-filling is studied by the time-dependent density matrix renormalization group method. It is clearly demonstrated that dielectric breakdown of the Mott insulating phase to a nonequilibrium steady state occurs when an external voltage is larger than the charge gap. From the numerically obtained current-voltage characteristics we find that the current is suppressed by the correlation effect when compared with that of a band insulator and that the current is scaled only by the charge gap for small voltages compared to the band width.

Journal of Physics Conference Series•Jan 1, 2011•0 citations

Nonequilibrium electronic transport in a one-dimensional Mott insulator

Fabian Heidrich‐Meisner, Iván González, K. A. Al-Hassanieh +3 more

We calculate the nonequilibrium electronic transport properties of a one-dimensional interacting chain at half filling, coupled to noninteracting leads. The interacting chain is initially in a Mott insulator state that is driven out of equilibrium by applying a strong bias voltage between the leads. For bias voltages above a certain threshold we observe the breakdown of the Mott insulator state and the establishment of a steady-state electronic current through the system. Based on extensive time-dependent density-matrix renormalization-group simulations, we show that this steady-state current always has the same functional dependence on voltage, independent of the microscopic details of the model and we relate the value of the threshold to the Lieb-Wu gap. We frame our results in terms of the Landau-Zener dielectric breakdown picture. Finally, we also discuss the real-time evolution of the current, and characterize the current-carrying state resulting from the breakdown of the Mott insulator by computing the double occupancy, the spin structure factor, and the entanglement entropy.

arXiv:1008.0101•Physical Review B•Nov 10, 2010•91 citations

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

Takashi Oka

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.

arXiv:1105.3145•Physical Review B•Aug 27, 2012•119 citations
Nonlinear transport of electrons in strong electric fields, as typified by dielectric breakdown, is reformulated in terms of the ground-state decay rate originally studied by Schwinger in nonlinear QED. We discuss the effect of electron interaction on Zener tunneling by comparing the dielectric breakdown of the band insulator and the Mott insulator, where the latter is studied by the time-dependent density-matrix renormalization group. The relation with the Berry's phase theory of polarization is also established.
The nonlinear transport properties of the Mott insulator are discussed with focus on the many-body Landau-Zener mechanism. After reviewing basic concepts such as the non-adiabatic geometric phase and the Schwinger mechanism, we study the decay of the insulating groundstate in strong electric fields using the time-dependent density matrix renormalization group. A short comment on the proposed mapping to the quantum walk model is added before discussing the relevance of the theory to experimental results. This article is a draft of a book chapter of the book entitled "Quantum and Semi-classical Percolation & Breakdown" (Lecture Note in Physics, Springer-Verlag), to appear 2008.
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.
Nonlinear response of a Mott insulator to external electric field, corresponding to dielectric breakdown phenomenon, is studied within of a one-dimensional half-filled Hubbard model. It is shown that in the limit of nearly spin-polarized insulator the decay rate of the ground state into excited holon-doublon pair can be evaluated numerically as well to high accuracy analytically. Results show that the threshold field depends on the charge gap as F(th)∝Δ(3/2). Numerical results on small systems indicate on the persistence of a similar mechanism for the breakdown for decreasing magnetization down to unpolarized system.
Nonequilibrium transport in the one dimensional Hubbard model at half-filling is studied by the time-dependent density matrix renormalization group method. It is clearly demonstrated that dielectric breakdown of the Mott insulating phase to a nonequilibrium steady state occurs when an external voltage is larger than the charge gap. From the numerically obtained current-voltage characteristics we find that the current is suppressed by the correlation effect when compared with that of a band insulator and that the current is scaled only by the charge gap for small voltages compared to the band width.
We calculate the nonequilibrium electronic transport properties of a one-dimensional interacting chain at half filling, coupled to noninteracting leads. The interacting chain is initially in a Mott insulator state that is driven out of equilibrium by applying a strong bias voltage between the leads. For bias voltages above a certain threshold we observe the breakdown of the Mott insulator state and the establishment of a steady-state electronic current through the system. Based on extensive time-dependent density-matrix renormalization-group simulations, we show that this steady-state current always has the same functional dependence on voltage, independent of the microscopic details of the model and we relate the value of the threshold to the Lieb-Wu gap. We frame our results in terms of the Landau-Zener dielectric breakdown picture. Finally, we also discuss the real-time evolution of the current, and characterize the current-carrying state resulting from the breakdown of the Mott insulator by computing the double occupancy, the spin structure factor, and the entanglement entropy.
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.