Stationary and dynamical descriptions of strong correlated systems

Abstract

This work is mainly devoted to the description of processes that involve the interaction between an atom and a surface, in which a strong Coulomb repulsion on the atomic site $(U)$ limits the charge exchange to one electron (infinite-$U$ limit). In this limit, the Anderson Hamiltonian for a many-fold $(N)$ of states localized on the atomic site can be represented in terms of auxiliary bosons and physical operators in the mixed boson-electron space can be defined. In this work the Hamiltonian is solved by defining appropriate Green's functions for physical operators. Then we solved the equations of motion of these Green's functions, up to a second order in the atom-surface coupling, either for the stationary case or for a real time-dependent problem. We show that our approach reproduces the known exact results in the nondegenerate $(N=1)$ case, and for $N\ensuremath{\succ}1$ gives excellent agreement with exact calculations and approximations valid for large $N$ (the $1∕N$ expansion). Finally, the accurate description of dynamical processes is shown by the comparison with the exact results available for a small four-level system. In this case we also compare with results obtained by using the noncrossing approximation and with the usual spinless model calculation.