Electron and phonon correlations in systems of one-dimensional electrons coupled to phonons are studied at low temperatures by emphasizing on the effect of electron-phonon backward scattering. It is found that the $2{k}_{F}$ -wave components of the electron density and phonon displacement field share the same correlations. Both correlations are quasi-long-ranged for a single conducting chain coupled to one-dimensional or three-dimensional phonons, and they are long-ranged for repulsive electron-electron interactions for a three-dimensional array of parallel one-dimensional conducting chains coupled to three-dimensional phonons.Electron and phonon correlations in systems of one-dimensional electrons coupled to phonons are studied at low temperatures by emphasizing on the effect of electron-phonon backward scattering. It is found that the $2{k}_{F}$-wave components of the electron density and phonon displacement field share the same correlations. Both correlations are quasi-long-ranged for a single conducting chain coupled to one-dimensional or three-dimensional phonons, and they are long-ranged for repulsive electron-electron interactions for a three-dimensional array of parallel one-dimensional conducting chains coupled to three-dimensional phonons.

arXiv:0806.0310Physical Review BNov 19, 20080 citations

One-dimensional electron-phonon system at arbitrary coupling constant

Larissa S. Brizhik, A. A. Eremko

Zeitschrift für Physik B Condensed MatterDec 1, 19979 citations

Quantum Field Lagrangian model for charge density waves in one-dimensional systems at finite temperature : A Thermofield Dynamics Approach

Luiz Victorio Belvedere, Rubens Gurgel Amaral, Armando Flavio Rodrigues

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 $U_e^5(1) \otimes U_{ph}(1)$ 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 $<0 (β) |Φ| 0 (β)> = 0$ , 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 $Ψ$ such that $<0 (β)| \barΨ(x)Ψ(x) | 0 (β)> \neq 0$ , without the breakdown of the linked electron-phonon symmetry.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 $U_e^5(1) \otimes U_{ph}(1)$ 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 $<0 (β) |Φ| 0 (β)> = 0$, 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 $Ψ$ such that $<0 (β)| \barΨ(x)Ψ(x) | 0 (β)> \neq 0$, without the breakdown of the linked electron-phonon symmetry.

arXiv:1204.4170Apr 18, 20120 citations

Variable-Range Hopping through Marginally Localized Phonons

Sumilan Banerjee, Ehud Altman

We investigate the effect of coupling Anderson localized particles in one dimension to a system of marginally localized phonons having a symmetry protected delocalized mode at zero frequency. This situation is naturally realized for electrons coupled to phonons in a disordered nanowire as well as for ultracold fermions coupled to phonons of a superfluid in a one-dimensional disordered trap. To determine if the coupled system can be many-body localized we analyze the phonon-mediated hopping transport for both the weak and strong coupling regimes. We show that the usual variable-range hopping mechanism involving a low-order phonon process is ineffective at low temperature due to discreteness of the bath at the required energy. Instead, the system thermalizes through a many-body process involving exchange of a diverging number n∝-logT of phonons in the low temperature limit. This effect leads to a highly singular prefactor to Mott's well-known formula and strongly suppresses the variable range hopping rate. Finally, we comment on possible implications of this physics in higher dimensional electron-phonon coupled systems.We investigate the effect of coupling Anderson localized particles in one dimension to a system of marginally localized phonons having a symmetry protected delocalized mode at zero frequency. This situation is naturally realized for electrons coupled to phonons in a disordered nanowire as well as for ultracold fermions coupled to phonons of a superfluid in a one-dimensional disordered trap. To determine if the coupled system can be many-body localized we analyze the phonon-mediated hopping transport for both the weak and strong coupling regimes. We show that the usual variable-range hopping mechanism involving a low-order phonon process is ineffective at low temperature due to discreteness of the bath at the required energy. Instead, the system thermalizes through a many-body process involving exchange of a diverging number n∝-logT of phonons in the low temperature limit. This effect leads to a highly singular prefactor to Mott's well-known formula and strongly suppresses the variable range hopping rate. Finally, we comment on possible implications of this physics in higher dimensional electron-phonon coupled systems.

arXiv:1511.03676Physical Review LettersMar 17, 201631 citations

2{k}_{F}

-wave components of the electron density and phonon displacement field share the same correlations. Both correlations are quasi-long-ranged for a single conducting chain coupled to one-dimensional or three-dimensional phonons, and they are long-ranged for repulsive electron-electron interactions for a three-dimensional array of parallel one-dimensional conducting chains coupled to three-dimensional phonons.

U_e^5(1) \otimes U_{ph}(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

, 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

Ψ

such that

<0 (β)| \barΨ(x)Ψ(x) | 0 (β)> \neq 0

, without the breakdown of the linked electron-phonon symmetry.