Properties of nonadiabatic quantum fluctuations of the strongly coupled electron-phonon systems

Abstract

A new variational-ansatz of states of electrons and phonons was proposed on the basis of the Holstein model in strongly coupled electron-phonon systems for studying the influence of nonadiabatic phonon fluctuation, arising from the motion and density fluctuation of electrons, on the properties of ground state, uncertainty relation, stability of polarons, charge density wave (CDW) and phonon staggered ordering. The new ansatz represents the correlation among the displacement and squeezing states of phonons and polaron’s state of electrons as well as the squeezing-antisqueezing effect. The correlation and squeezing-antisqueezing effect result in the decrease of ground state energy, enhancement of stability of the systems, increase of binding energy of the polarons, weakening of the growing speed of polaron narrowing of the electron band, increase of the charge density wave order and suppression of the increased tendency of anomalous quantum fluctuation of the phonons in such a case, when compared with the uncorrelated case in the systems. The results obtained show that the ground state determined by the new state ansatz is most stable, thus the new ansatz describing the properties of the coupled electron phonon systems is very relevant and available, especially in strongly coupled and largely squeezed cases.