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arXiv:1002.1863 · Physical Review B

Charge-density-wave formation in a half-filled fermion-boson transport model: A projective renormalization approach

Steffen Sykora, K. W. Becker, Holger Fehske

Published May 27, 2010• 7 citations
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Abstract

We study the metal-insulator transition in a very general two-channel transport model, where charge carriers are coupled to a correlated background medium. The fluctuations of the background were described as bosonic excitations, having the ability to relax. Employing an analytical projector-based renormalization technique, we calculate the ground-state and spectral properties of this fermion-boson model and corroborate recent numerical results, which indicate---in dependence on the ``stiffness'' of the background medium---a Luttinger liquid to charge-density-wave transition for the one-dimensional half-filled band case. In particular, we determine the renormalized electron and boson dispersion relations and show that the quantum phase transition is not triggered by a softening of the boson modes. Thus, the charge density wave is different in nature from an usual Peierls distorted state.

DOI
10.1103/physrevb.81.195127

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We study the metal-insulator transition in a very general two-channel transport model, where charge carriers are coupled to a correlated background medium. The fluctuations of the background were described as bosonic excitations, having the ability to relax. Employing an analytical projector-based renormalization technique, we calculate the ground-state and spectral properties of this fermion-boson model and corroborate recent numerical results, which indicate---in dependence on the ``stiffness'' of the background medium---a Luttinger liquid to charge-density-wave transition for the one-dimensional half-filled band case. In particular, we determine the renormalized electron and boson dispersion relations and show that the quantum phase transition is not triggered by a softening of the boson modes. Thus, the charge density wave is different in nature from an usual Peierls distorted state.
We solve a very general two-channel fermion-boson model describing charge transport within some background medium by means of a refined pseudosite density-matrix renormalization group technique. Performing a careful finite-size scaling analysis, we determine the ground-state phase diagram and convincingly prove that the model exhibits a metal-insulator quantum phase transition for the half-filled band case. In order to characterize the metallic and insulating regimes we calculate, besides the local particle densities and fermion-boson correlation functions, the kinetic energy, the charge-structure factor, the Luttinger liquid charge exponent, and the single-particle excitation gap for a one-dimensional infinite system.
We investigate charge transport within some background medium by means of an effective lattice model with a novel form of fermion-boson coupling. The bosons describe fluctuations of a correlated background. By analyzing ground state and spectral properties of this transport model, we show how a metal-insulator quantum phase transition can occur for the half-filled band case. We discuss the evolution of a mass-asymmetric band structure in the insulating phase and establish connections to the Mott and Peierls transition scenarios.
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.
To understand how charge transport is affected by a background medium and vice versa we study a two-channel transport model which captures this interplay via a novel, effective fermion-boson coupling. By means of (dynamical) DMRG we prove that this model exhibits a metal-insulator transition at half-filling, where the metal typifies a repulsive Luttinger liquid and the insulator constitutes a charge density wave. The quantum phase transition point is determined consistently from the calculated photoemission spectra, the scaling of the Luttinger liquid exponent, the charge excitation gap, and the entanglement entropy.
We analyze the spectral properties of a very general two-channel fermion-boson transport model in the insulating and metallic regimes and the signatures of the metal-insulator quantum phase transition in between. To this end we determine the single-particle spectral function related to angle-resolved photoemission spectroscopy, the momentum distribution function, the Drude weight, and the optical response by means of a dynamical (pseudosite) density-matrix renormalization group technique for the one-dimensional half-filled band case. We show how the interplay of correlations and fluctuations in the background medium controls the charge dynamics of the system, which is a fundamental problem in a great variety of advanced materials.
Including the previously ignored dispersion of phonons we revisit the metal-insulator transition problem in one-dimensional electron-phonon systems on the basis of a modified spinless fermion Holstein model. Using matrix-product-state techniques we determine the global ground-state phase diagram in the thermodynamic limit for the half-filled band case, and show that in particular the curvature of the bare phonon band has a significant effect, not only on the transport properties characterized by the conductance and the Luttinger liquid parameter, but also on the phase space structure of the model as a whole. While a downward curved (convex) dispersion of the phonons only shifts the Tomonaga-Luttinger-liquid to charge-density-wave quantum phase transition towards stronger EP coupling, an upward curved (concave) phonon band leads to a new phase-separated state which, in the case of strong dispersion, can even completely cover the charge-density wave. Such phase separation does not occur in the related Edwards fermion-boson model.