Properties of ground state and anomalous quantum fluctuations in one-dimensional polaron—soliton systems—the effects of electron-two-phonon interaction and non-adiabatic quantum correlations

Abstract

Based on the Holstein model Hamiltonian of one-dimensional molecular crystals, by making use of the expansion approach of the correlated squeezed-coherent states of phonon instead of the two-phonon coherent state expansion scheme, the properties of the ground state and the anomalous quantum fluctuations are investigated in a strongly coupled electron—phonon system with special consideration of the electron-two-phonon interaction. The effective renormalization (α̃i) of the displacement of the squeezed phonons with the effect of the squeezed-coherent states of phonon and both the electron-displaced phonon and the polaron-squeezed phonon correlations have been combined to obtain the anomalous quantum fluctuations for the corrections of the coherent state. Due to these non-adiabatic correlations, the effective displacement parameter α̃i is larger than the ordinary parameter αi(0). In comparison with the electron-one-phonon interaction (g) corrected as α̃ig, we have found the electron-two-phonon interaction (g1) corrected as α̃i2g1 is enhanced significantly. For this reason, the ground state energy (E0(2)) contributed by the electron-two-phonon interaction is more negative than the single-phonon case (E0(1)) and the soliton solution is more stable. At the same time, the effects of the electron-two-phonon interaction greatly increase the polaron energy and the quantum fluctuations. Furthermore, in a deeper level, we have considered the effect of the polaron-squeezed phonon correlation (f-correlation). Since this correlation parameter f > 1, this effect will strengthen the electron-one and two-phonon interactions by fα̃ig and f2α̃i2g1, respectively. The final results show that the ground state energy and the polaron energy will appear more negative further and the quantum fluctuations will gain further improvement.