Functional renormalization group approach to the Anderson impurity model

Details Functional renormalization group approach to the Anderson impurity model Functional renormalization group approach to the Anderson impurity model

2008-11-18

arxiv.org/abs/0811.2809v1

Journal of Physics: Condensed Matter 21, 305602 (2009).

Physics

Condensed Matter

Strongly Correlated Electrons

15 pages, 16 figures

Scientific paper

10.1088/0953-8984/21/30/305602

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 Sch\"{u}tz, 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.

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