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Journal of Physics Condensed Matter

Effect of electric field on one-dimensional insulators: a density matrix renormalization group study

Sudipta Dutta, S. Lakshmi, Swapan Kumar Pati

Published Jun 27, 2007• 13 citations
Publisher

Abstract

We perform density matrix renormalization group (DMRG) calculations extensively on one-dimensional Mott and Peierls chains with explicit inclusion of the static bias to study the insulator–metal transition in those systems. We find that the electric field induces a number of insulator–metal transitions for finite-size systems and, at the thermodynamic limit, the insulating system breaks down into a completely conducting state at a critical value of bias that depends strongly on the insulating parameters. Our results indicate that the breakdown, in both the Peierls and Mott insulators, at the thermodynamic limit, does not follow the Landau–Zener mechanism. Calculations on various size systems indicate that an increase in the system size decreases the threshold bias as well as the charge gap at that bias, making the insulator–metal transition sharper in both cases.

DOI
10.1088/0953-8984/19/32/322201

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We perform density matrix renormalization group (DMRG) calculations extensively on one-dimensional Mott and Peierls chains with explicit inclusion of the static bias to study the insulator–metal transition in those systems. We find that the electric field induces a number of insulator–metal transitions for finite-size systems and, at the thermodynamic limit, the insulating system breaks down into a completely conducting state at a critical value of bias that depends strongly on the insulating parameters. Our results indicate that the breakdown, in both the Peierls and Mott insulators, at the thermodynamic limit, does not follow the Landau–Zener mechanism. Calculations on various size systems indicate that an increase in the system size decreases the threshold bias as well as the charge gap at that bias, making the insulator–metal transition sharper in both cases.
We perform density matrix renormalization group (DMRG) calculations extensively on one dimensional Mott and Peierls chains with explicit inclusion of the static bias to study the insulator-metal transition in those systems. We find that the electric field induces a number of insulator-metal transitions for finite size systems and at the thermodynamic limit, the insulating system breaks down into a completely conducting state at a critical value of bias which depends strongly on the insulating parameters. Our results indicate that the breakdown, in both the Peierls and Mott insulators, at thermodynamic limit, does not follow the Landau-Zener mechanism. Calculations on various size systems indicate that an increase in the system size decreases the threshold bias as well as the charge gap at that bias, making the insulator-metal transition sharper in both cases.
We perform density matrix renormalization group calculations extensively on one-dimensional chains with on-site ( U ) as well as nearest-neighbour ( V ) Coulomb repulsions. The calculations are carried out in full parameter space with explicit inclusion of the static bias and we compare the nature of spin-density-wave (SDW) and charge-density-wave (CDW) insulators under the influence of external electric fields. We find that, although the SDW ( U >2 V ) and CDW ( U <2 V ) insulators enter into a conducting state after a certain threshold bias, CDW insulators require much higher bias than the SDW insulators for insulator–metal transitions at zero temperature. We also find the CDW–SDW phase transition on application of an external electric field. The bias required for the transitions in both cases decreases with increase in system size.
The current-voltage characteristics and mechanism of bias-induced breakdown in one-dimensional models for band and Mott insulators are investigated theoretically by using nonequilibrium Green’s functions. We attach the models to metallic electrodes, the effects of which are incorporated into the self-energy. For the models of both the band and the Mott insulators with lengths L C , the bias voltage induces a breakdown of the insulating state, and the breakdown mechanism shows a crossover depending on L C . When L C is smaller than the correlation length ξ = W/Δ, the threshold is determined basically by the bias V th ∼ Δ, where W and Δ are the bandwidth and the energy gap, respectively. For systems with L C ≫ ξ, the threshold is governed by the electric field, V th/L C , which is consistent with a Landau-Zener-type breakdown V th/L C ∝ Δ2/W.
Nonequilibrium states induced by an applied bias voltage (V)(V)(V) and the corresponding current-voltage characteristics of one-dimensional models describing band and Mott insulators are investigated theoretically by using nonequilibrium Green's functions. We attach the models to metallic electrodes, the effects of which are incorporated into the self-energy. Modulation of the electron density and the scalar potential coming from the additional long-range interaction are calculated self-consistently within the Hartree approximation. For both models of band and Mott insulators with length LC{L}_{C}LC​, the bias voltage induces a breakdown of the insulating state, the threshold of which shows a crossover depending on LC{L}_{C}LC​. It is determined basically by the bias ${V}_{\mathrm{th}}~\ensuremath{\Delta}$ for LC{L}_{C}LC​ smaller than the correlation length $\ensuremath{\xi}=W/\ensuremath{\Delta}$, where WWW denotes the bandwidth and $\ensuremath{\Delta}$ denotes the energy gap. For systems with ${L}_{C}\ensuremath{\gg}\ensuremath{\xi}$, the threshold is governed by the electric field Vth/LC{V}_{\mathrm{th}}/{L}_{C}Vth​/LC​, which is consistent with a Landau-Zener--type breakdown ${V}_{\mathrm{th}}/{L}_{C}\ensuremath{\propto}{\ensuremath{\Delta}}^{2}/W$. We demonstrate that the spatial dependence of the scalar potential is crucially important for this crossover by showing the case without the scalar potential, where the breakdown occurs at ${V}_{\mathrm{th}}~\ensuremath{\Delta}$ regardless of the length LC{L}_{C}LC​.
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.
We investigate three different types of quantum phase transition occurring in quasi one-dimensional systems theoretically and numerically. First, we study the band-insulator to Mott-insulator transition occurring in charge-transfer complexes, for which the half-filled one-dimensional ionic Hubbard model is considered to be the prototype model. The study is carried out by first deriving an effective spin-one model, and then studying the model numerically using the density matrix renormalization group. We perform a careful finite-size scaling analysis of the mass gaps, order-parameters, and relative susceptibility. We confirm the existence of two quantum critical points. Analysis of the critical exponents confirms that the band-insulator-to-spontaneously-dimerized phase transition belong to the 2D Ising class. The spontaneously dimerized phase undergoes a phase transition to the Mott-insulator which is an infinite-order. Second, we investigate the Mott metal-insulator transition for the half-filled Hubbard model with both nearest-neighbor t and next-nearest-neighbor t′ hopping terms. We study the model using the bosonization approach and density matrix renormalization group simulations. An effective low-energy Hamiltonian that describes the insulator-metal transition is derived. We present results of density matrix renormalization group calculations of spin and charge distribution in various sectors of the phase diagram. The numerical results support the picture derived from the effective theory and give evidence for the complete separation of the transitions involving the spin and the charge degrees of freedom. Finally, we investigate quantum phase transitions phases in low-dimensional fermionic and spin models that go from uniform to spatially inhomogeneous, i.e., dimerized, trimerized, or incommensurate, phases. We propose a new approach based on studying the length dependence of the von Neumann entropy and its corresponding Fourier spectrum for finite segments in the ground state of finite chains. Peaks at a nonzero wave vector are indicators of oscillatory behavior in decaying correlation functions and also provide significant information about certain relevant features of the excitation spectrum; in particular, they can identify the wave vector of soft modes in critical models.