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Abstract:
Non-Hermitian degeneracies are classified as defective exceptional points (EPs) and nondefective de- generacies. While in defective EPs, both eigenvalues and eigenvectors coalesce, nondefective degeneracies are characterized merely by the emergence of degenerate eigenvalues. It is also known that all degeneracies are either symmetryprotected or accidental. In this paper, I prove that antiunitary symmetries protect all nondefective twofold degeneracies. By developing a 2D non-Hermitian tight-binding model, I have demonstrated that these symmetries comprise 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 degeneracies in various parameter regimes of my model. This work paves the way to stabilizing nondefective degeneracies and offers a new perspective on understanding non-Hermitian band crossings.
