Functional renormalization group for non-Hermitian and $\mathcal{PT}$-symmetric systems

TL;DR

This paper extends the functional renormalization group vertex expansion method to non-Hermitian and $ ext{PT}$-symmetric systems, demonstrating its viability through an exactly solvable toy model.

Contribution

It generalizes the vertex expansion approach to non-Hermitian systems and assesses its effectiveness using a solvable $ ext{PT}$-symmetric model.

Findings

Vertex expansion is viable for non-Hermitian systems.

Fidelity of the method is comparable to Hermitian cases.

Additional flow terms appear due to non-Hermiticity.

Abstract

We generalize the vertex expansion approach of the functional renormalization group to non-Hermitian systems. As certain anomalous expectation values might not vanish, additional terms as compared to the Hermitian case can appear in the flow equations. We investigate the merits and shortcomings of the vertex expansion for non-Hermitian systems by considering an exactly solvable $\mathcal{PT}$-symmetric non-linear toy-model and reveal, that in this model, the fidelity of the vertex expansion in a perturbatively motivated truncation schema is comparable with that of the Hermitian case. The vertex expansion appears to be a viable method for studying correlation effects in non-Hermitian systems.