Correlated electron-phonon systems: Variational approaches

U. Trapper, Holger Fehske, Martin Deeg +1 more

V. A. Moskalenko

Takahiro Ohgoe, Masatoshi Imada

We develop a variational Monte Carlo (VMC) method for electron-phonon coupled systems. The VMC method has been extensively used for investigating strongly correlated electrons over the last decades. However, its applications to electron-phonon coupled systems have been severely restricted because of its large Hilbert space. Here, we propose a variational wave function with a large number of variational parameters, which is suitable and tractable for systems with electron-phonon coupling. In the proposed wave function, we implement an unexplored electron-phonon correlation factor, which takes into account the effect of the entanglement between electrons and phonons. The method is applied to systems with diagonal electron-phonon interactions, i.e., interactions between charge densities and lattice displacements (phonons). As benchmarks, we compare VMC results with previous results obtained by the exact diagonalization, the Green function Monte Carlo method and the density matrix renormalization group for the Holstein and Holstein-Hubbard model. From these benchmarks, we show that the present method offers an efficient way to treat strongly coupled electron-phonon systems.

Pang Xiao‐feng

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.

Eric Jeckelmann, Chunli Zhang, Steven R. White

Chi‐Fai Lo, Efstratios Manousakis, Roger Sollie +1 more

We have investigated the ground state of an electron-phonon system with strong electron-phonon interaction and a weak on-site Coulomb repulsion using the correlated squeezed-state approach. We have introduced a variational ground state in which the phonon subsystem is in a correlated squeezed state and the electron subsystem is in a superconducting pairing state. In addition to the anharmonicity of each phonon mode induced by the linear coupling with the electrons, the correlated squeezed state is able to take into account the nonlinearity of the induced interaction between different phonon modes beyond the Hartree approximation. Also, with optimal values of the variational parameters this trial state will by construction yield an energy lower than those obtained in previous studies, and thus our variational ansatz is a more stable ground state for this system. Furthermore, in this approximate ground state the 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; for instance, it does suggest the possibility of higher critical temperatures for superconductivity in the strong-coupling limit where the superfluidlike bipolaronic superconductivity is supposed to occur.