Strongly Interacting Quasiparticle-Boson Systems: Validity of Approximation Schemes

С.П. Иванова, R. V. Jolos, R. Pedrosa

O. V. Danylenko, O. V. Dolgov

We investigate effects of a nonadiabatic electron-phonon(boson) interaction on the quasiparticle self-energy in the lowest order in the coupling constant. Existing approaches either overestimate or underestimate these effects because of different approximations for momentum and frequency dependences of the vertex corrections. The connection between the nonadiabaticity and a possible instability of the interacting Fermi system is discussed as well.

M. I. Salkola, A. R. Bishop, V. M. Kenkre +1 more

The validity of the semiclassical approximation is studied for a system comprising one quasiparticle coupled to a boson degree of freedom. Using a two-site Holstein model as an example, it is shown that the semiclassical approximation becomes exact in a nontrivial adiabatic limit. Furthermore, in the model's polaron regime, there exists a hierarchy of time scales that rationalizes the quantum dynamics of the Holstein model. For the single-mode case considered, the discrete nonlinear Schr\"odinger equation is found to be valid only in a highly limited antiadiabatic regime.

M. Binder

J. Ruvalds

Andrei E. Ruckenstein, Stefan Schmitt-Rink

We introduce a new approach to strongly correlated systems, based on equations of motion for composite ("quasiparticle") operators. Conserving approximations to the appropriate Green's functions are generated through functional differentiation. For illustration, we apply this scheme to the infinite-$U$, single-band Hubbard model. The analogue of the Hartree-Fock approximation becomes exact in the limit of infinite spin degeneracy ($N$), while the random-phase approximation leads to the corresponding $\frac{1}{N}$ fluctuations.