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Physical review. B, Condensed matter

Correlated squeezed-state approach for a dissipative two-state system

Chi‐Fai Lo, W. H. Wong

Published Aug 1, 1995• 10 citations
Publisher

Abstract

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.

DOI
10.1103/physrevb.52.3333

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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.
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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.
We have investigated the ground state of an electron-phonon system with strong electron-phonon interaction and a weak on-site Coulomb repulsion using the correlated squeezed-state approach. We have introduced a variational ground state in which the phonon subsystem is in a correlated squeezed state and the electron subsystem is in a superconducting pairing state. In addition to the anharmonicity of each phonon mode induced by the linear coupling with the electrons, the correlated squeezed state is able to take into account the nonlinearity of the induced interaction between different phonon modes beyond the Hartree approximation. Also, with optimal values of the variational parameters this trial state will by construction yield an energy lower than those obtained in previous studies, and thus our variational ansatz is a more stable ground state for this system. Furthermore, in this approximate ground state the 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; for instance, it does suggest the possibility of higher critical temperatures for superconductivity in the strong-coupling limit where the superfluidlike bipolaronic superconductivity is supposed to occur.