Solution of the Anderson impurity model via the functional renormalization group

TL;DR

This paper demonstrates that the functional renormalization group is an efficient and accurate method for analyzing the low-energy properties of the Anderson impurity model, matching Bethe ansatz results.

Contribution

It introduces a numerically inexpensive FRG approach using an external magnetic field and partial bosonization to study the Anderson impurity model.

Findings

Accurately computes quasi-particle residue and spin susceptibility.

Shows excellent agreement with Bethe ansatz results.

Provides a practical method for low-energy impurity physics.

Abstract

We show that the functional renormalization group is a numerically cheap method to obtain the low-energy behavior of the Anderson impurity model describing a localized interacting electron coupled to a bath of conduction electrons. Our approach uses an external magnetic field as flow parameter, partial bosonization of the transverse spin fluctuations, and frequency-independent interaction vertices which are fixed by Ward identities. We calculate the quasi-particle residue and the spin susceptibility in the particle-hole symmetric case and obtain excellent agreement with the Bethe ansatz results for arbitrary strengths of the interaction.