  In this paper we have explored the role of valence fluctuations in an
extended Anderson impurity model (e-SIAM) in which there is an additional
Hubbard repulsion between conduction and impurity electrons, employing
perturbative renormalization methods. We have calculated the scaling equations
for the model parameters and solved them both analytically and numerically to
find how valence fluctuations renormalize these parameters. Analytical
solutions of the scaling equations yielded scaling invariants of the model
which we find to be different than the Anderson impurity model signifying
different kind of scaling trajectories of e-SIAM. The strong coupling physics
of SIAM is known to be governed by spin fluctuations and we hence analysed how
the strong coupling regime of e-SIAM is renormalized by valence fluctuations.
Doing a third order perturbative renormalization of the model gave us access to
the Kondo scale. We not only confirmed that valence fluctuations enhance the
Kondo scale but we also calculated the functional form of this dependence.
Benchmarking some of our results with numerical renormalization group
calculations, we found excellent agreement. Applying Schrieffer-Wolff
transformation, we found that the strong coupling regime of the model is
governed by spin-charge Kondo model unlike the Anderson impurity model. Our
results suggest that spin Kondo effect can co-exist with valence fluctuation
mediated charge Kondo effect.
