Protection of all nondefective twofold degeneracies by anti-unitary symmetries in non-Hermitian systems

TL;DR

This paper proves that anti-unitary symmetries can protect all nondefective twofold exceptional points in non-Hermitian systems, using a 2D tight-binding model to demonstrate their stabilization across various parameters.

Contribution

It introduces a theoretical framework showing anti-unitary symmetries protect nondefective EPs, expanding understanding of symmetry protection in non-Hermitian band structures.

Findings

Anti-unitary symmetries protect all nondefective twofold EPs.

Composite symmetries include discrete, spatial, and Wick rotations.

Protection demonstrated across various parameter regimes.

Abstract

Non-Hermitian degeneracies are classified as defective and nondefective exceptional points~(EP). While in defective EPs, both eigenvalues and eigenenergies coalesce, nondefective EPs are characterized merely by the occurrence of degeneracies in their eigenvalues. It is also known that all degeneracies are either symmetry-protected or accidental. In this paper, I prove that anti-unitary symmetries protect all nondefective twofold EPs. By developing a 2D non-Hermitian tight-binding model, I have demonstrated that these symmetries are composite of various symmetry operations such as discrete or spatial point-group symmetries and Wick's rotation in the non-Hermitian parameter space. Introducing these composite symmetries, I present the protection of nondefective EPs in various parameter regimes of my model. This work paves the way to stabilizing nondefective EPs and offers a new perspective on understanding non-Hermitian band crossings.