Renormalization group flow for fermions into antiferromagnetically ordered phases: Method and mean-field models

TL;DR

This paper develops a functional renormalization group method for fermionic lattice models that captures antiferromagnetic phases, reproduces mean-field results, and introduces a more efficient vertex parametrization for complex models.

Contribution

It introduces a fermionic vertex-based RG flow approach for antiferromagnetic phases and proposes an improved vertex parametrization for broader applicability.

Findings

Reproduces mean-field results for long-range interactions

Shows how anisotropies affect the RG flow

Proposes a more efficient vertex decomposition method

Abstract

We present a functional renormalization group flow for many-fermion lattice models into phases with broken spin-rotational symmetry. The flow is expressed purely in terms of fermionic vertex functions. The symmetry breaking is seeded by a small initial anomalous self-energy which grows at the transition scale and which prevents a runaway-flow at nonzero scales. Focusing on the case of commensurate antiferromagnetism we discuss how the interaction vertex can be parametrized efficiently. For reduced models with long-range bare interactions we show the results of standard mean-field theory are reproduced by the fRG and how anisotropies in the spin sector change the flows. We then describe a more efficient decomposition of the interaction vertex that should allow for the treatment of more general models.