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Il Nuovo Cimento D

Correlated squeezed-state approach for the ground state of strongly correlated electrons coupled to local Holstein phonons

Anders Kristoffersen, Chi‐Fai Lo, Roger Sollie

Published Aug 1, 1996• 1 citation
Publisher
DOI
10.1007/bf02459075

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physica status solidi (b)•Feb 1, 2000•3 citations
Effects of the nonadiabatic phonon fluctuations on the ground state of coupled one-dimensional electron-phonon systems with high and low electron-densities were investigated by a new ansatz including correlated interaction of the displacement and squeezing. The correlated effect resulted in noticeable reduction of ground state energy of the systems, and obvious increases of binding energy of the polarons occurred. Thus, the stabilities of the polaron and of the systems were significantly enhanced, exactly steady ground state of the Holstein model, then, was obtained by the new ansatz for the coupled electron-phonon systems. In general, the new ansatz were found to be very relevant for the strong coupling and large squeezing cases in nonadiabatically coupled electron-photon systems.
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.
The influences of the squeezing–antisqueezing effect arising from variations of the electron density and motion of polarons and nonadiabatic phonon fluctuations on the properties of the ground state and the binding energy of the polaron in the Holstein model of coupled one-dimensional electron–phonon systems with spin 1/2 in the cases of high and low electron densities have been studied by using the Bogolyubov transformation and a new ansatz for states that includes correlation effects among the one-phonon coherent and two-phonon squeezed and polaronic states. The results obtained show that the squeezing–antisqueezing (correlation) effect results in that the ground state energy of the systems is significantly lowered, and the binding energy of the polaron is considerably increased. Thus, the stability of the systems and of the polaron are obviously enhanced in such a case when compared with the uncorrelated case. This shows that the ground state determined by the new state ansatz is most stable, and the new ansatz introduced here is very relevant for the coupled electron–phonon systems, especially in strongly coupled and largely squeezed cases.