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

• URL: http://arxiv.org/abs/2605.28351v1
• Date: Wed, 27 May 2026 11:53:20 GMT
• Title: Quantum geometry of connected state manifolds: When diabolic points act as bridges between eigenstate manifolds
• Abstract summary: We regularise the metric by a coordinate transformation and develop a formalism in which diabolic points act as bridges between adjacent eigenstate manifold.<n>We characterise the topology of this structure and refine the rules for nodal lines governing the Berry phase.<n>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.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

Related papers

• State--Generator Geometry of Open Quantum Systems: Compatibility and Covariant Transport [0.0]
  We develop a geometry for transporting stationary-state response across the control space of an open quantum system.<n>We compute the connection by automatic differentiation through the stationary Liouvillian Bloch solve and recover the symbolic result to machine precision.
  arXiv  Detail & Related papers  (2026-08-19T17:52:08Z)
• Symmetry-protected topology and deconfined solitons in a multi-link $\mathbb{Z}_2$ gauge theory [45.88028371034407]
  We study a $mathbbZ$ lattice gauge theory defined on a multi-graph with links that can be visualized as great circles of a spherical shell.<n>We show that this leads to state-dependent tunneling amplitudes underlying a phenomenon analogous to the Peierls instability.<n>By performining a detailed analysis based on matrix product states, we prove that charge deconfinement emerges as a consequence of charge-fractionalization.
  arXiv  Detail & Related papers  (2026-03-02T22:59:25Z)
• Geometry-driven transitions in sparse long-range spin models with cold atoms [0.3079885946230076]
  We examine a model with interactions that can be continuously tuned to induce distinct changes in the metric, topology, and dimensionality of the coupling graph.<n>This underlying geometry acts as the driver of criticality, with structural changes in the graph coinciding with and dictating the phase boundaries.<n>In certain cases, the effective geometry can be incorporated in the layout of atoms in tweezers to realize phase transitions that preserve universal features.
  arXiv  Detail & Related papers  (2025-12-09T15:24:27Z)
• Symmetric Localizable Multipartite Quantum Measurements from Pauli Orbits [39.3098730337656]
  We introduce a general approach to construct highly symmetric, locally encodable orthonormal measurement bases.<n>We show how the symmetry of our constructions allows us to characterize their localizability, which is generally a challenging problem.<n>Our approach offers a systematic toolkit for designing entangled measurements with rich symmetry and implementability properties.
  arXiv  Detail & Related papers  (2025-09-02T00:37:28Z)
• Scaling of Quantum Geometry Near the Non-Hermitian Topological Phase Transitions [0.0]
  We unveil diverse scalings of the quantum geometry over the ground state manifold close to different topological phase transitions.<n>Near certain criticalities, we find that the Wannier state correlation function associated with extended Berry connection of the ground state exhibits spatially anomalous behaviors.
  arXiv  Detail & Related papers  (2025-05-06T03:56:48Z)
• Quantum geometry in many-body systems with precursors of criticality [0.0]
  We analyze the geometry of the ground-state manifold in parameter-dependent many-body systems with quantum phase transitions (QPTs)<n>We elucidate the role of diabolic points in the formation of first-order QPTs, showing that these isolated geometric singularities represent seeds generating irregular behavior of geodesics in finite systems.
  arXiv  Detail & Related papers  (2024-11-06T15:06:05Z)
• Action formalism for geometric phases from self-closing quantum trajectories [55.2480439325792]
  We study the geometric phase of a subset of self-closing trajectories induced by a continuous Gaussian measurement of a single qubit system. We show that the geometric phase of the most likely trajectories undergoes a topological transition for self-closing trajectories as a function of the measurement strength parameter.
  arXiv  Detail & Related papers  (2023-12-22T15:20:02Z)
• Tuning long-range fermion-mediated interactions in cold-atom quantum simulators [68.8204255655161]
  Engineering long-range interactions in cold-atom quantum simulators can lead to exotic quantum many-body behavior. Here, we propose several tuning knobs, accessible in current experimental platforms, that allow to further control the range and shape of the mediated interactions.
  arXiv  Detail & Related papers  (2022-03-31T13:32:12Z)
• Higher-order topological states mediated by long-range coupling in $D_4$-symmetric lattices [0.0]
  Topological physics opens a door towards flexible routing and resilient localization of waves of various nature. Recently proposed higher-order topological insulators provide advanced control over wave localization in the structures of different dimensionality. Here, we design and experimentally realize the resonant electric circuit with $D_4$ symmetry and additional next-nearest-neighbor couplings.
  arXiv  Detail & Related papers  (2021-03-16T11:15:54Z)
• Models of zero-range interaction for the bosonic trimer at unitarity [91.3755431537592]
  We present the construction of quantum Hamiltonians for a three-body system consisting of identical bosons mutually coupled by a two-body interaction of zero range. For a large part of the presentation, infinite scattering length will be considered.
  arXiv  Detail & Related papers  (2020-06-03T17:54:43Z)
• Bulk detection of time-dependent topological transitions in quenched chiral models [48.7576911714538]
  We show that the winding number of the Hamiltonian eigenstates can be read-out by measuring the mean chiral displacement of a single-particle wavefunction. This implies that the mean chiral displacement can detect the winding number even when the underlying Hamiltonian is quenched between different topological phases.
  arXiv  Detail & Related papers  (2020-01-16T17:44:52Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.