Interaction of conduction electrons with local excitations. The infrared divergencies

Abstract

Using the renormalization group method the higher orders of perturbation theory in the interaction of conduction electrons in metals with local paulions (pseudospins), e.g. two-level systems, crystal-field excitations, and bosons, e.g. phonons, are considered. For the paulions, the lowest order logarithmic singularities in the electron self-energy at ɛ=E−EF→±Δ, Δ being the splitting, become weaker, at least in the commutative model. It is shown that the singularities of the type ln ɛ are absent. This justifies the applicability of the second order perturbation theory resultm* ∼Δ−1 for the electron effective mass even atm*≫m. For the phonons, the singularities at e→±ω0, ω0 being the phonon frequency, may become stronger or weaker depending on the conduction band filling and the anharmonic contribution to the deformation potential. The singular contributions to the local excitation Green's function are calculated. They result in the change of the line shape of the local level (the “orthogonality catastrophe”). The singular terms in the ground state energy and average pseudospin are considered.