Encircling an exceptional point once changes a transported quantum state by an order-four operator, so the exceptional point acts as a topological defect in the full Hilbert space bundle.
Znojil, Features, Paradoxes and Amendments of Perturbative Non-Hermitian Quantum Mechanics , Symmetry 16, 629 (2024)
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Evidence for Exceptional Points as Topological Defects
Encircling an exceptional point once changes a transported quantum state by an order-four operator, so the exceptional point acts as a topological defect in the full Hilbert space bundle.