Exactly solvable models of unconventional magnetic alloys: Bethe ansatz versus renormalization-group method

We propose toy models of unconventional magnetic alloys, in which the density of band states, ρ(ɛ), and hybridization, t(ɛ), are energy dependent; it is assumed, however, that t²(ɛ)~ρ^-1(ɛ), and hence an effective electron-impurity coupling Γ(ɛ)=ρ(ɛ)t²(ɛ) is energy independent. In the renormalization-group approach, the physics of the system is assumed to be governed by Γ(ɛ) only rather than by separate forms of ρ(ɛ) and t(ɛ). However, an exact Bethe ansatz solution of the toy Anderson model demonstrates a crucial role of a form of inverse band dispersion k(ɛ).