Quantum fluctuations in correlated electron systems

Takashi Yanagisawa, Izumi Hase

罗质华, 曹锡金, 余超凡

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 ( 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 i is larger than the ordinary parameter α i (0) . In comparison with the electron-one-phonon interaction ( g ) corrected as i g , we have found the electron-two-phonon interaction ( g 1 ) corrected as 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 f i g and f 2 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.

Anatoli Polkovnikov

Norikazu Tomita, Shuji Watanabe, Keisuke Shida +2 more

Large quantum fluctuations in the strongly correlated electron systems as well as electron-phonon coupled systems are visualized by the resonating Hartree-Fock (HF) method). We show that, in the two-dimensional Hubbard model, doped holes form topological defects called polarons. It is also shown that the quantum fluctuations drastically change the lattice structures in the Su-Schrieffer-Heeger model.

Pavel V. Shevchenko

A. F. Th. Hoekstra, John A. Mydosh