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

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.