Functional renormalization group approach to the Anderson impurity model

Abstract

We develop a functional renormalization group approach which describes the low-energy single-particle properties of the Anderson impurity model up to intermediate on-site interactions $U\lesssim 15\Delta$, where $\Delta$ is the hybridization in the wide-band limit. Our method is based on a generalization of a method proposed by Schütz, Bartosch and Kopietz [Phys. Rev. B 72, 035107 (2005)], using two independent Hubbard-Stratonovich fields associated with transverse and longitudinal spin fluctuations. Although we do not reproduce the exponentially small Kondo scale in the limit $U\to \infty$, the spin fluctuations included in our approach remove the unphysical Stoner instability predicted by mean-field theory for $U>\pi \Delta$. We discuss different decoupling schemes and show that a decoupling which manifestly respects the spin-rotational invariance of the problem gives rise to the lowest quasiparticle weight. To obtain a closed flow equation for the fermionic self-energy we also propose a new truncation scheme of the functional renormalization group flow equations using Dyson-Schwinger equations to express bosonic vertex functions in terms of fermionic ones.

15 pages, 16 figures

References in corpus (6)

• The numerical renormalization group method for quantum impurity systems
• Collective fields in the functional renormalization group for fermions, Ward identities, and the exact solution of the Tomonaga-Luttinger model
• Renormalization group flow for fermionic superfluids at zero temperature
• Antiferromagnetism and single-particle properties in the two-dimensional half-filled Hubbard model: Slater vs Mott-Heisenberg
• Kondo behavior in the asymmetric Anderson model: Analytic approach
• Effective action for superfluid Fermi systems in the strong-coupling limit

Cited by in corpus (1)

• Renormalization of the BCS-BEC crossover by order parameter fluctuations