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arXiv:0801.0414 · Journal of Physics Condensed Matter

External electric field mediated quantum phase transitions in one-dimensional charge-ordered insulators: a density matrix renormalization group study

Sudipta Dutta, Swapan K Pati

Published Jan 31, 2008• 7 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1088/0953-8984/20/7/075226

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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.
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.
In order to clarify the physics of the crossover from a spin-density-wave (SDW) Mott insulator to a charge-density-wave (CDW) Peierls insulator in one-dimensional (1D) systems, we investigate the Hubbard-Holstein Hamiltonian at half filling within a density matrix renormalisation group (DMRG) approach. Determining the spin and charge correlation exponents, the momentum distribution function, and various excitation gaps, we confirm that an intervening metallic phase expands the SDW-CDW transition in the weak-coupling regime.
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.
We examine the ground-state properties of the one-dimensional Edwards spinless fermion transport model by means of large-scale density-matrix renormalization-group calculations. Determining the single-particle gap and the Tomonaga-Luttinger liquid parameter (KρK_ρKρ​) at zero temperature, we prove the existence of a metal-to-insulator quantum phase transition at one-third band filling. The insulator---established by strong correlation in the background medium---typifies a charge density wave (CDW) that is commensurate with the band filling. Kρ=2/9K_ρ=2/9Kρ​=2/9 is very small at the quantum critical point, and becomes KρCDW=1/9K_ρ^{\rm CDW}=1/9KρCDW​=1/9 in the infinitesimally doped three-period CDW, as predicted by the bosonization approach.
The charge-density-wave (CDW)--spin-density-wave (SDW) phase transition of the one-dimensional extended Hubbard model is investigated in the strong correlation regime, from the viewpoint of the quantum coherence or decoherence of the two correlated states. In the finite-size system, the CDW wave function, near the phase boundary, has the significant quantum fluctuations due to the SDW domains. The superposition of these SDW domains leads to the quantum coherence between the CDW and SDW wave functions. However, the scaling analysis shows that the density of the SDW fluctuations becomes asymptotically zero in the infinite-size limit, which indicates the decoherence of the two states in the bulk phase transition.