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

Luo Zhi-Hua^{a}, Yu Chao-Fan^{a}, Cao Xi-Jin^{b}

^{a} Department of Physics, Guangdong University of Education, Guangzhou 510303, China; ^{b} Pinggang Middle School, Longgang District, Shenzhen 518116, China

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 (ã_{i}) 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 ã_{i} is larger than the ordinary parameter α_{i}^{(0)}. In comparison with the electron-one-phonon interaction (g) corrected as ã_{i}, we have found the electron-two-phonon interaction (g_{1}) corrected as ã_{i}^{2}g_{1} is enhanced significantly. For this reason, the ground state energy (E_{0}^{(2)}) contributed by the electron-two-phonon interaction is more negative than the single-phonon case (E_{0}^{(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 fã_{i}g and f^{2}ã_{i}^{2}g_{1}, 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.

Luo Zhi-Hua,Cao Xi-Jin,Yu Chao-Fan. 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[J]. Chin. Phys. B, 2011, 20(6):067103.