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Physical Review A

Variational study of the linear Jahn-Teller effect: Case of an electronic doublet interacting with a doubly degenerate vibration

Chi‐Fai Lo

Published May 1, 1991• 30 citations
Publisher

Abstract

A variational study of the linear E-e Jahn-Teller effect, in which an electronic doublet interacts with a doubly degenerate vibration, has been performed using a simple correlated trial ground-state wave function--a correlated squeezed state. Our calculated variational ground-state energies are not only in good agreement with the exact diagonalization results, but they are also better than those from earlier analytical studies. This seems to suggest that the linear E-e Jahn-Teller system favors a strongly correlated squeezed ground state.

DOI
10.1103/physreva.43.5127

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A variational study of the linear E-e Jahn-Teller effect, in which an electronic doublet interacts with a doubly degenerate vibration, has been performed using a simple correlated trial ground-state wave function--a correlated squeezed state. Our calculated variational ground-state energies are not only in good agreement with the exact diagonalization results, but they are also better than those from earlier analytical studies. This seems to suggest that the linear E-e Jahn-Teller system favors a strongly correlated squeezed ground state.
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In this work we have applied the optimal coupled-cluster approximation to study the ground state of the E⊗(b1+b2) Jahn–Teller effect. The effectiveness of the optimal coupled-cluster approximation has been investigated for the whole range of the asymmetry parameter and various coupling strengths. It is shown that our results up to the third level of approximation are in very good agreement with the exact numerical diagonalization results and are better than those from earlier variational treatments. Furthermore, unlike previous variational treatments, the optimal coupled-cluster approximation has the advantage that the accuracy of both the ground state energy and wavefunction estimates is being taken care of and can be systematically improved. Since the mathematical treatment in this work is simple, the optimal coupled-cluster approximation could be easily extended to the studies of other fermion-boson interacting systems, e.g. the extended Jahn–Teller system.
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.
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