Bosonic effective action for interacting fermions

TL;DR

This paper explores various bosonic descriptions of interacting fermion systems, emphasizing symmetry and functional methods, including exact mappings, systematic expansions, and renormalization group approaches for improved theoretical understanding.

Contribution

It introduces a systematic bosonic effective action framework with exact mappings and a novel functional renormalization group formulation for interacting fermions.

Findings

Exact mapping between repulsive and attractive interactions in the Hubbard model

Proposal of a renormalized gap equation for beyond leading order calculations

Comparison of bosonic and partially bosonized renormalization approaches

Abstract

We compare different versions of a bosonic description for systems of interacting fermions, with particular emphasis on the free energy functional. The bosonic effective action makes the issue of symmetries particularly transparent and we present for the Hubbard model an exact mapping between repulsive and attractive interactions. A systematic expansion for the bosonic effective action starts with a solution to the lowest order Schwinger-Dyson or gap equation. We propose a two particle irreducible formulation of an exact functional renormalization group equation for computations beyond leading order. On this basis we suggest a renormalized gap equation. This approach is compared with functional renormalization in a partially bosonized setting.