Eur. Phys. J. B (2014) 87: 262
https://doi.org/10.1140/epjb/e2014-50464-x

Regular Article

Renormalized perturbation theory flow equations for the Anderson impurity model

Department of Mathematics, Imperial College London, London SW7 2AZ, UK

^a e-mail: vassilis.pandis@gmail.com

Received: 8 July 2014
Received in final form: 10 September 2014
Published online: 5 November 2014

Abstract

We apply the renormalized perturbation theory (RPT) to the symmetric Anderson impurity model. Within the RPT framework exact results for physical observables such as the spin and charge susceptibility can be obtained in terms of the renormalized values µ̃ = (Δ̃, Ũ) of the hybridization Δ and Coulomb interaction U of the model. The main difficulty in the RPT approach usually lies in the calculation of the renormalized values themselves. In the present work we show how this can be accomplished by deriving differential flow equations describing the evolution of µ̃(Δ) with Δ. By exploiting the fact that µ̃(Δ) can be determined analytically in the limit Δ → ∞ we solve the flow equations numerically to obtain estimates for the renormalized parameters in the range 0 <U/πΔ< 3.5.