Flow-Equation method for a superconductor with magnetic correlations

TL;DR

This paper applies the flow equation method to analyze a superconductor with magnetic correlations, revealing how impurity energy depends on renormalized parameters and showing the irrelevance of s-d interactions at strong Hubbard repulsion.

Contribution

It introduces the use of the flow equation method to study impurity energies in superconductors with magnetic correlations, highlighting the dependence on renormalized parameters.

Findings

Impurity energy depends only on the squared renormalized order parameter.

At strong Hubbard repulsion, s-d interactions become irrelevant.

The method confirms expected behavior for strong Hubbard interactions.

Abstract

The flow equation method has been used to calculate the energy of single impurity in a superconductor for the Anderson model with $U \neq 0$. We showed that the energy of the impurity depends only of the $\Delta^{2}_{R}$ (renormalized order parameter) which depends on the renormalized Hubbard repulsion$U^R$. For a strong Hubbard repulsion $U^R = U$ and $\Delta^R = \Delta ^I$ the effect of the $s-d$ interactions are nonrelevant, a result which is expected for this model.