Effect of electron-phonon interaction and external magnetic field on the bound state in the Anderson-Holstein model: an improved variational treatment

Abstract

The single-impurity Anderson-Holstein model is investigated in the presence of a magnetic field by an improved variational method. The phonon degrees of freedom are first eliminated by a modified Lang-Firsov transformation followed by a zero-phonon averaging. The resulting Hamiltonian is then treated by a cluster variational method to study the effects of the electron-phonon interaction and the magnetic field on the ground state energy, local magnetic moment and the binding energy between the magnetic impurity and the conduction electrons.