Symmetry protected exceptional points of interacting fermions

TL;DR

This paper studies how symmetry protected exceptional points in non-hermitian fermionic systems behave under interactions, revealing their stability, new interaction-induced points, and annihilation phenomena, supported by an exceptional perturbation theory.

Contribution

It demonstrates that symmetry protected exceptional points remain stable with interactions, introduces interaction-induced exceptional points, and describes their annihilation, advancing understanding of non-hermitian many-body physics.

Findings

Exceptional points are stable under fermionic interactions.

Interaction can generate new exceptional points from degeneracies.

Exceptional points can annihilate each other at parameter space intersections.

Abstract

Non-hermitian quantum systems can exhibit spectral degeneracies known as exceptional points, where two or more eigenvectors coalesce, leading to a non-diagonalizable Jordan block. It is known that symmetries can enhance the abundance of exceptional points in non-interacting systems. Here, we investigate the fate of such symmetry protected exceptional points in the presence of a symmetry preserving interaction between fermions and find that, (i) exceptional points are stable in the presence of the interaction. Their propagation through the parameter space leads to the formation of characteristic exceptional ``fans''. In addition, (ii) we identify a new source for exceptional points which are only present due to the interaction. These points emerge from diagonalizable degeneracies in the non-interacting case. Beyond their creation and stability, (iii) we also find that exceptional points can annihilate each other if they meet in parameter space with compatible many-body states forming a third order exceptional point at the endpoint. These phenomena are well captured by an ``exceptional perturbation theory'' starting from a non-interacting Hamiltonian.