Abstract
We discuss Kondo effect for a general model, describing a quantum impurity with degenerate energy levels, interacting with a gas of itinerant electrons, and derive scaling equation to the second order for such a model. We show how the scaling equation for the spin-anisotropic Kondo model with the power law density of states (DOS) for itinerant electrons follows from the general scaling equation. We introduce the anisotropic Coqblin–Schrieffer model, apply the general method to derive scaling equation for that model for the power law DOS, and integrate the derived equation analytically.
Highlights
Observed under appropriate conditions logarithmic increase of the scattering of the itinerant electrons by an isolated magnetic impurity was explained in 1964 in a seminal paper by Kondo, entitled ”Resistance Minimum in Dilute Magnetic Alloy”1
The models where the density of states (DOS) of itinerant electrons in the vicinity of the Fermi level is the power function of energy has attracted a lot of interest5–11
Following the long line of works where spin-anisotropic Kondo model was studied3,10,13,14, we decided to revisit the problem of scaling equation for the Kondo effect in general4, and introduce and study the anisotropic Coqblin–Schrieffer (CS) model15 in particular
Summary
Because all the integrals with respect to energy in perturbation series terms are understood in the Principal Value sense, the denominator going to zero is by itself not a problem, and the second order terms just gives a correction to the matrix element of the order of the ratio of the scattering energy V to the band width (we consider electron band ǫ ∈ [−D0, D0] and assume that the ratio is V /D is small). Each of the second order terms in Eq [4] contains large logarithmic multiplier ln(ǫ/D0), because of strongly asymmetric range of integration; due to the existence of the impurity quantum numbers, these terms do not add up to Eq [5]
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