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International Journal of Modern Physics B

CHARGE-DENSITY-WAVES IN THE PRESENCE OF IMPURITY POTENTIAL IN ONE-DIMENSIONAL SYSTEMS: A FIELD THEORY APPROACH

L. V. Belvedere, R. L. P. G. Amaral, A. F. DE QUEIROZ

Published Mar 10, 2004• 1 citation
Publisher

Abstract

The effective Lagrangian model for charge-density waves interacting with an impurity potential in one-dimensional systems is considered in the dynamical phonon phase approach. Using the fermion–boson mapping we obtain the effective bosonized version of the model. The impurity potential breaks the linked electron–phonon symmetry, the phason field turns out to be in interaction with the electron–phonon condensate and the phonon field develops a non-vanishing vacuum expectation value. The effective fermionized version of the model corresponds to the chiral Gross–Neveu model with quartic self-interaction among a massless and a massive (electron) Fermi fields. The electron–phonon system exhibits a conserved topological charge which is independent of local variations of the phases of the phonon and electron fields. The equation of state of the associated statistical-mechanical system is obtained. For the dynamical phonon phase field the Kosterlitz–Thouless phase transition is suppressed.

DOI
10.1142/s0217979204023994

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The effective Lagrangian model for charge-density waves interacting with an impurity potential in one-dimensional systems is considered in the dynamical phonon phase approach. Using the fermion–boson mapping we obtain the effective bosonized version of the model. The impurity potential breaks the linked electron–phonon symmetry, the phason field turns out to be in interaction with the electron–phonon condensate and the phonon field develops a non-vanishing vacuum expectation value. The effective fermionized version of the model corresponds to the chiral Gross–Neveu model with quartic self-interaction among a massless and a massive (electron) Fermi fields. The electron–phonon system exhibits a conserved topological charge which is independent of local variations of the phases of the phonon and electron fields. The equation of state of the associated statistical-mechanical system is obtained. For the dynamical phonon phase field the Kosterlitz–Thouless phase transition is suppressed.
We use the two-dimensional Fermion-Boson mapping to perform a field theory analysis of the effective Lagrangian model for incommensurate charge-density waves (ICDW) in one-dimensional systems. We consider an approach in which both the phase of the complex phonon field and the electron field are dynamical degrees of freedom contributing to the quantum dynamics and symmetry-related features of the ICDW phenomenon. We obtain the bosonized and fermionized versions of the effective electron–phonon Lagrangian. The phase of the phonon field and the phase of the bosonized chiral density of the electron field condense as a soliton order parameter, carrying neither the charge nor the chirality of the electron–phonon system, leading to a periodic sine-Gordon potential. The phonon field is fermionized in terms of a chiral fermionic condensate and the effective model is mapped into the chiral Gross–Neveu (GN) model with two Fermi field species. The linked electron–phonon symmetry of the ICDW system is mapped into the chiral symmetry of the GN model. Within the functional integral formulation, we obtain for the vacuum expectation value of the phonon field < ϕ > = 0 and < ϕ ϕ* > ≠ 0, due to the charge selection rule associated with the chiral electron–phonon symmetry. We show that the two-point correlation function of the phonon field satisfies the cluster decomposition property, as required by the chiral symmetry of the underlying GN model. The quantum description of the ICDW corresponds to charge transport through the lattice, due to the propagation of a "Goldstone mode" carrying the effective charge of the electron–phonon system, is accomplished by an electron–lattice energy redistribution. This accounts for a dynamical Peierls's energy gap generation.
We consider the Thermofield Dynamics bosonization to perform a field theory analysis of the effective Lagrangian model for incommensurate charge density waves (ICDW) in one-dimensional systems at finite temperature. The phonon degree of freedom is carryied by a dynamical phase field, contributing to the quantum dynamics and symmetry related features of the ICDW phenomenon. The electron chiral density and the phase of the phonon field condensate as a thermal soliton, carrying the symmetry under the linked electron-phonon Ue5(1)⊗Uph(1)U_e^5(1) \otimes U_{ph}(1)Ue5​(1)⊗Uph​(1) global transformations. Using the Gell'Mann-Low formula for finite temperature, the perturbative series of the phonon thermal correlation function is obtained. Due to the electron-phonon charge selection rule we obtain for the thermal vacuum expectation value for the order parameter <0(β)∣Φ∣0(β)>=0<0 (β) |Φ| 0 (β)> = 0<0(β)∣Φ∣0(β)>=0, in accordance with the cluster decomposition property of the corresponding correlation function. This reflects the fact that the quantum description of the ICDW corresponds to a local charge transport through the lattice which is accomplished by an electron-lattice energy redistribution, which accounts for a thermal dynamical mass gap generation. The electron-phonon coupling can be rewritten in terms of a mass operator for the "physical" fermion operator ΨΨΨ such that <0(β)∣Ψˉ(x)Ψ(x)∣0(β)>≠0<0 (β)| \barΨ(x)Ψ(x) | 0 (β)> \neq 0<0(β)∣Ψˉ(x)Ψ(x)∣0(β)>=0, without the breakdown of the linked electron-phonon symmetry.
Electrons in one-dimensional disordered systems exhibit Anderson localization in the absence of mutual interactions. However the transition is possible between localized and delocalized state as the interaction is turned on. In this paper such interplay between Anderson localization and interactions has been examined for spin dependent Tomonaga model based on the phase Hamiltonian derived by the bosonization of the fermion field. The problem is the extention of the classical impurity pinning of the charge density wave to that of quantum systems with phase variables of not only charge but also spin. The critical value of the interaction constant has been derived by the use of selfconsistent-harmonic approximation to the nonlinearity.
The formation of charge-density-wave order in Dirac fermion systems via electron-phonon coupling represents a significant topic in condensed matter physics. In this work, we investigate this phenomenon within the Holstein model on the honeycomb lattice, with a specific focus on the effect of disorder. While the interplay between electron-electron interactions and disorder has long been a central theme in the field, recent attention has increasingly turned to the combined influence of disorder and electron-phonon coupling. Using determinant quantum Monte Carlo simulations, we concentrate on the phase transitions of charge-density-wave order on the honeycomb lattice. Disorder is introduced through the random hopping of electrons in the system, which can localize electrons via the Anderson effect. Our primary result is that disorder suppresses the charge-density-wave phase, and the interplay between disorder and electron-phonon interactions extends the phase area. We also determine the transition temperature βcβ_cβc​ to the ordered phase as a function of the electron-phonon coupling. Additionally, we observed a suppression of electron kinetic energy and dc conductivity under disorder, highlighting the role of Anderson localization in the degradation of electronic transport. These findings offer significant theoretical insight into the stability and critical phenomena of correlated phases in disordered two-dimensional systems.
We apply a recently proposed path-integral approach to non-local bosonization to a Thirring-like system modeling non-relativistic massless particles interacting with localized fermionic impurities. We consider forward-scattering processes described by symmetric potentials including interactions between charge, current, spin and spin-current densities. In the general (spin-flipping) problem we obtain an effective action for the collective modes of the model at T = 0, containing WZW-type terms. When spin-flipping processes are disregarded the structure of the action is considerably simplified, allowing us to derive exact expressions for the dispersion relations of collective modes and two-point fermionic correlation functions as functionals of the potentials. Finally, as an example, we compute the momentum distribution for the case in which electrons and impurities are coupled through spin and spin-current densities only. The formulae we get suggest that our formalism could be useful in order to seek for a mechanism able to restore Fermi liquid behavior.
The spontaneous generation of charge-density-wave order in a Dirac fermion system via the natural mechanism of electron-phonon coupling is studied in the framework of the Holstein model on the honeycomb lattice. Using two independent and unbiased quantum Monte Carlo methods, the phase diagram as a function of temperature and coupling strength is determined. It features a quantum critical point as well as a line of thermal critical points. Finite-size scaling appears consistent with fermionic Gross-Neveu-Ising universality for the quantum phase transition and bosonic Ising universality for the thermal phase transition. The critical temperature has a maximum at intermediate couplings. Our findings motivate experimental efforts to identify or engineer Dirac systems with sufficiently strong and tunable electron-phonon coupling.