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Topological Quantum Computing Open Quantum Systems Decoherence Quantum Simulation

Quantum geometry of connected state manifolds: When diabolic points act as bridges between eigenstate manifolds

arXiv

Authors: Jan Střeleček, Jakub Novotný, Pavel Cejnar

Year

2026

Paper ID

68178

Status

Preprint

Abstract Read

~2 min

Abstract Words

109

Citations

Abstract

Parametric Hamiltonians often exhibit point-like spectral degeneracies (diabolic points, or conical intersections), which can lead to singularities in the Provost-Vallee metric of eigenstate manifolds. We regularise the metric by a coordinate transformation and develop a formalism in which diabolic points act as bridges between adjacent eigenstate manifolds, glueing them into a single connected state manifold. We characterise the topology of this structure and refine the rules for nodal lines governing the Berry phase. The connected state manifold restores the numerical stability near diabolic points, enlarges the class of geodesics allowing for new geodesic shortcuts, and provides a new mechanism for Berry phase computation, even along paths traversing diabolic points.

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Parametric Hamiltonians often exhibit point-like spectral degeneracies (diabolic points, or conical intersections), which can lead to singularities in the Provost-Vallee metric...

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References & Citation Signals

[1] DOI https://doi.org/arXiv:2605.28351 [2] arXiv https://arxiv.org/abs/2605.28351 [3] Publisher https://arxiv.org/abs/2605.28351

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