Ward identities for the Anderson impurity model: derivation via functional methods and the exact renormalization group

TL;DR

This paper derives Ward identities for the Anderson impurity model using functional methods and the exact renormalization group, providing a non-perturbative proof of key low-energy relations.

Contribution

It offers a non-perturbative derivation of Yamada-Yosida identities linking self-energy coefficients to susceptibilities, highlighting symmetry relations.

Findings

Non-perturbative proof of Yamada-Yosida identities

Relation of identities to U(1) x U(1) symmetry

Clarification of low-energy expansion coefficients

Abstract

Using functional methods and the exact renormalization group we derive Ward identities for the Anderson impurity model. In particular, we present a non-perturbative proof of the Yamada-Yosida identities relating certain coefficients in the low-energy expansion of the self-energy to thermodynamic particle number and spin susceptibilities of the impurity. Our proof underlines the relation of the Yamada-Yosida identities to the U(1) x U(1) symmetry associated with particle number and spin conservation in a magnetic field.