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Physical review. B, Condensed matter

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

Chi‐Fai Lo, Roger Sollie

Published Sep 1, 1991• 20 citations
Publisher

Abstract

A variational study of a tunneling particle coupled to phonons is presented. The trial wave function has built in the correlation between different modes and thereby goes beyond earlier variational treatments. This leads to a significant improvement of the energy and therefore a better representation of the ground state. The condition for the localization-delocalization transition of the tunneling particle is modified in the correlated squeezed state compared to previous studies.

DOI
10.1103/physrevb.44.5013

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Physical review. B, Condensed matter•Oct 1, 1993•18 citations
A variational study of a tunneling particle coupled to phonons is presented. The trial wave function has built in the correlation between different modes and thereby goes beyond earlier variational treatments. This leads to a significant improvement of the energy and therefore a better representation of the ground state. The condition for the localization-delocalization transition of the tunneling particle is modified in the correlated squeezed state compared to previous studies.
We propose a correlated squeezed-state approach to study the dissipative two-state system at zero temperature. We have found that the ground state of this system can be better described by the correlated squeezed-state ansatz than those given in earlier variational treatments. In this new ground state the suppression effect of the phonon overlapping integral on the renormalized tunneling parameter is much more alleviated. Thus, the condition for the localization-delocalization transition of the two-state system is significantly modified in this correlated squeezed state, when compared with previous studies.
The ground states of phonons in a dissipative quantum tunneling system and their influences on the localiza ion-delocalization transtion are investigated by a variational approach. We find that: 1. There are two kind of influences, displacement and deformation, on phonon states due to coupling with a tunneling particle, and displaced -squeezed states are proposed to describe both these influences. 2. The localization-delocahzation transition depends on the choice of phonon ground state. The transition will occur at strong coupling as the energy of the ground state decreases.
The variational approach is applied to the study of the ground state of quantum tunneling system interacting with two phonons by use of a correlated-squeezed transformation. We fine: 1) For the two phonons bath, the ground state energy of the phonons with correlation effect is lower than that without correlation effect; 2) The effect of correlation varies with the mode parameters: In the resonant regime of the phonons and two-state system, the correlation effect is more significant and will be strengthened together with the increase of coupling coefficient.
In this paper we have applied the correlated squeezed-state approach to investigate the ground-state properties of the one-dimensional Hubbard model with a local Holstein-type electron-phonon interaction. We have introduced a variational ground state in which the phonon subsystem is in a correlated squeezed state. The correlated squeezed state has built in the correlation between different phonon modes induced by the linear coupling with the electrons. With optimal values of the variational parameters the correlated squeezed state will by construction yield an energy lower than those obtained in earlier treatments. This means that our variational ansatz is more stable as the ground state of the system. Furthermore, our variational study shows that in the correlated squeezed state the polaronic reduction effect of phonons is much more alleviated, and thus the mass enhancement inherent to the polaron effect is considerably weakened. This weakening of the reduction effect should, in turn, affect other physical properties of the system.