Evidence for Exceptional Points as Topological Defects

Quantum 10, 2220 (2026). https://doi.org/10.22331/q-2026-09-30-2220 Studies have shown that quantum states reside in a Hilbert space bundle. When a quantum system depends on continuous external parameters, these parameters define additional dimensions in the base space of the bundle. While much of the existing literature focuses on eigenstate subbundles, where geometric properties like Berry curvature arise, this work considers the entire Hilbert space bundle. Although the Hilbert space bundle has been found to be locally flat, suggesting that the system's topology may appear trivial, we revisit this assumption. Specifically, we examine how an arbitrary quantum state evolves when transported along closed parameter loops, a phenomenon characterized by holonomy. Our results demonstrate that nontrivial holonomy can emerge in the presence of exceptional points. Consequently, exceptional points naturally manifest as topological defects. Finally, we show that this nontrivial topology manifests in physical, time-dependent evolutions, providing a simple experimental signature to detect exceptional points by comparing state transport along distinct paths.

Studies have shown that quantum states reside in a Hilbert space bundle. When a quantum system depends on continuous external parameters, these parameters define additional dimensions in the base space of the bundle. While much of the existing literature focuses on eigenstate subbundles, where geometric properties like Berry curvature arise, this work considers the entire Hilbert space bundle. Although the Hilbert space bundle has been found to be locally flat, suggesting that the system's topology may appear trivial, we revisit this assumption. Specifically, we examine how an arbitrary quantum state evolves when transported along closed parameter loops, a phenomenon characterized by holonomy. Our results demonstrate that nontrivial holonomy can emerge in the presence of exceptional points. Consequently, exceptional points naturally manifest as topological defects. Finally, we show that this nontrivial topology manifests in physical, time-dependent evolutions, providing a simple experimental signature to detect exceptional points by comparing state transport along distinct paths.

This study reveals how exceptional points in quantum systems act as topological defects that alter the entire Hilbert space bundle. Although Berry connections, curvatures, and phases are useful for studying state evolution along a path in parameter space, certain issues occur when encircling an exceptional point. Therefore, rather than focusing on a specific Hamiltonian eigenstate, this work takes the full Hilbert space into account and computes the holonomy for quantum states without applying the adiabatic approximation. While standard quantum states return to their original form after traveling a closed parameter loop, loops that enclose exceptional points do not. Moreover, these anomalies leave distinct, measurable physical signatures and footprints in real time-dependent quantum evolutions depending on the path taken. Ultimately, this unified mathematical framework could pave the way for advanced quantum control and robust qubit manipulation.

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Evidence for Exceptional Points as Topological Defects

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