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.

• Received 21 March 1994

DOI:https://doi.org/10.1103/PhysRevB.50.418