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International Journal of Modern Physics B

Properties of the Squeezed Polarons in One Dimension

Xiyu Su, Hang Zheng

Published Sep 10, 1998• 2 citations
Publisher

Abstract

An electron related squeezed phonon transformation is employed to investigate the ground state properties of the strongly coupled electron–phonon system in one dimension. It has been shown that the binding energy of the polaron and the interaction between the polarons are renormalized together with the energy reducement of the electron subsystem resulted from the squeeze state of the phonon subsystem. Some relevance with the earlier variational treatments has been discussed as well.

DOI
10.1142/s0217979298001290

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International Journal of Modern Physics B•Dec 30, 2003•0 citations
An electron related squeezed phonon transformation is employed to investigate the ground state properties of the strongly coupled electron–phonon system in one dimension. It has been shown that the binding energy of the polaron and the interaction between the polarons are renormalized together with the energy reducement of the electron subsystem resulted from the squeeze state of the phonon subsystem. Some relevance with the earlier variational treatments has been discussed as well.
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.
The effects of the nonadiabatic phonon behaviours on the ground state of the system and the quantum modifications of the polaron characteristics and the modification form of the uncertainty relation between the phonon coordinate and momentum due to fluctuations of the electron density in the coupled electron-phonon systems have been studied by using a new variational ansatz for coherent phonons with correlated displacement and squeezing including internations with electrons. The correlated effect results in the following effect: (1) the energy of the ground state of the system is found to be lower than that for the phonons with uncorrelated displacement and squeezing; (2) the binding energy of the polaron was found to be increased; (3) the nonadiabatic coupling with electrons enhances the quantum uncertainty for the phonon coordinate and momentum when compared with the adiabatic and uncorrelated case.
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.
Changes in the physical properties such as the ground state properties, charge density wave ordering, binding energy and energy bandwidth of polaron and quantum fluctuation, and minimum uncertainty relation of phonons and nonadiabatically coupled electron–phonon systems with spin-1/2 have been investigated by our new state ansatz which can account for correlation among the phononic displacement, squeezing and polaron effects using variational method in one-dimensional Holstein model. The investigation here shows that the squeezing–antisqueezing effect (correlated) results in a decrease of the ground state energy, an increase of the binding energy of polarons, the reduction of the uncertainty and quantum fluctuation of the phonons, a decrease of polaron narrowing of electron bandwidth, an increase of tunneling effect of the polarons and an increase of CDW ordering and phonon staggered ordering when compared with the uncorrelated case. Therefore, this shows that the ground state determined by the new state ansatz is the most stable. The new ansatz which include the squeezing–antisqueezing (correlated) effect is very relevant for the coupled electron–phonon systems, especially in strongly coupled and highly squeezed cases.