Quantum geometry of connected state manifolds: When diabolic points act as bridges between eigenstate manifolds
Abstract
Parametric Hamiltonians often exhibit point-like spectral degeneracies, called diabolic points (DPs) or conical intersections, which can lead to singularities in the Provost-Vallee metric of eigenstate manifolds. We regularise the metric by a transformation to polar coordinates and develop a formalism in which DPs act as bridges between adjacent eigenstate manifolds, glueing them into a single connected state manifold (CSM). We characterise the topology of this structure and extend the local rules for nodal lines governing the Berry phase to global ones. On the CSM, the class of geodesics can be enlarged by those passing through the DPs. They can be stable with respect to their initial direction, and can be shorter than those constrained to a single eigenstate manifold, providing new geodesic shortcuts. Further, the CSM provides a new mechanism for Berry phase computation along paths traversing the DPs.
Related
- Quantum field theory and four-manifolds: Perspectives from physics and geometry
- On the mapping class groups of simply connected smooth 4-manifolds
- h-cobordisms between $1$-connected manifolds with boundary
- Non-concordant 2-links in simply-connected 4-manifolds
- Self-intersecting sections of polar actions on simply connected manifolds
BibTeX
@misc{strelecek2026quantum,
title = {{Quantum geometry of connected state manifolds: When diabolic points act as bridges between eigenstate manifolds}},
author = {Jan Střeleček and Jakub Novotný and Pavel Cejnar},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2605.28351},
eprint = {2605.28351},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.28351},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Quantum geometry of connected state manifolds: When diabolic points act as bridges between eigenstate manifolds
AU - Jan Střeleček
AU - Jakub Novotný
AU - Pavel Cejnar
PY - 2026
DA - 2026/10/19
PB - arXiv
DO - 10.48550/arxiv.2605.28351
UR - https://arxiv.org/abs/2605.28351
AB - Parametric Hamiltonians often exhibit point-like spectral degeneracies, called diabolic points (DPs) or conical intersections, which can lead to singularities in the Provost-Vallee metric of eigenstate manifolds. We regularise the metric by a transformation to polar coordinates and develop a formalism in which DPs act as bridges between adjacent eigenstate manifolds, glueing them into a single connected state manifold (CSM). We characterise the topology of this structure and extend the local rules for nodal lines governing the Berry phase to global ones. On the CSM, the class of geodesics can be enlarged by those passing through the DPs. They can be stable with respect to their initial direction, and can be shorter than those constrained to a single eigenstate manifold, providing new geodesic shortcuts. Further, the CSM provides a new mechanism for Berry phase computation along paths traversing the DPs.
ER -