Correlations in non-Hermitian systems and Diagram techniques for the steady state

TL;DR

This paper introduces a diagrammatic technique for analyzing correlations in non-Hermitian fermionic systems at steady state, revealing how interactions displace nodal features and break symmetry protections.

Contribution

It presents a novel diagrammatic method for non-Hermitian steady states, enabling systematic study of correlation effects and symmetry breaking in such systems.

Findings

Nodal objects are displaced in momentum-space due to interactions.

Exceptional points break certain orthonormal symmetries.

The method applies to exceptional points and rings in non-Hermitian systems.

Abstract

We describe a diagrammatic technique for non-Hermitian fermionic systems that is applicable in the steady state, and which allows addressing correlations effects by systematic expansion. Applying this method to exceptional points or rings, we find that nodal objects in non-Hermitian systems are generically displaced in momentum-space due to interactions. This in turn can be connected to the fact that exceptional points invariably break a class of orthonormal symmetries that are generally present for nodal points in Hermitian systems, and which protect the integrity of the node at low energy scales.