Squeezed-state approach for phonon coupling in tunneling systems at zero temperature

In the present paper we propose a method of studying a two-state system coupled linearly to a boson field with complex coupling in a correlated squeezed state approach. The complex coupling leads to the initiation of complex probability density with complex statistical averages. Exploiting the biorthonormal formalism we obtain the analytical forms of the complex expectation value E of H as well as the complex tunneling reduction factor. As it is seen from our results the localization–delocalization transition of the tunneling particle is modified for small values of the real part of the coupling constant in comparison with the conventional (g real) correlated squeezed state approach.

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Correlated-squeezed-state approach for phonon coupling in a tunneling system

Physical Review B ◽

10.1103/physrevb.44.5013 ◽

1991 ◽

Vol 44 (10) ◽

pp. 5013-5015 ◽

Cited By ~ 18

Author(s):

C. F. Lo ◽

R. Sollie

Keyword(s):

Phonon Coupling ◽

Squeezed State ◽

Tunneling System

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Polaron Crystallization and the Metal–Insulator Transition

International Journal of Modern Physics B ◽

10.1142/s0217979298002210 ◽

1998 ◽

Vol 12 (29n31) ◽

pp. 3131-3136 ◽

Cited By ~ 10

Author(s):

P. Quémerais ◽

S. Fratini

Keyword(s):

Physical Mechanism ◽

Insulator Transition ◽

Vibrational Modes ◽

Zero Temperature ◽

Phonon Coupling ◽

Metal Insulator Transition ◽

Strong Electron ◽

Metal Insulator ◽

Electron Phonon Coupling ◽

Polar Materials

The Crystallization of polarons at finite density, due to the long-range Coulomb forces — when no bipolarons can be formed — is discussed close to the metal–insulator transition (MIT). As a function of the density, the melting is examined at zero temperature. By calculating the quantum fluctuations of both the electron and the polarization, we show that at strong electron–phonon coupling the dissociation of the polarons at the MIT is favored, rather than the melting towards a polaron liquid. In this regime, we demonstrate, that an instability of the transverse vibrational modes of the polaron crystal occurs as the density increases. This provides a new physical mechanism for the MIT in polar materials, for which an experimental signature is predicted.

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Wilson's Numerical Renormalization Group Calculation of the Anderson–Holstein Model: Phonon Propagator

International Journal of Modern Physics B ◽

10.1142/s0217979203021046 ◽

2003 ◽

Vol 17 (18n20) ◽

pp. 3381-3386 ◽

Cited By ~ 1

Author(s):

Han-Yong Choi ◽

Tae-Ho Park ◽

Gun Sang Jeon

Keyword(s):

Renormalization Group ◽

Phonon Mode ◽

Soft Mode ◽

Coulomb Repulsion ◽

Zero Temperature ◽

Coupling Constant ◽

Phonon Coupling ◽

Improved Method ◽

Numerical Renormalization Group ◽

Electron Phonon Coupling

We study the symmetric Anderson–Holstein (AH) model at zero temperature with Wilson's numerical renormalization group (NRG) technique to study the interplay between the electron-electron and electron-phonon interactions. An improved method for calculating the phonon propagator using the NRG technique is presented and applied to the AH model as the onsite Coulomb repulsion U and electron-phonon coupling constant g are varied. As g is increased, the phonon propagator is successively renormalized, and for g≳gco crosses over to the regime where the mode splits into two components, one of which approaches back to the bare frequency and the other develops into a soft mode. The initial renormalization of the phonon mode, as g is increased from 0, can be either positive or negative depending on U and the hybridization Δ.

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