Exceptional-Point Geometry of Weak Topological Boundary States

• URL: http://arxiv.org/abs/2607.21148v1
• Date: Thu, 23 Jul 2026 10:30:37 GMT
• Title: Exceptional-Point Geometry of Weak Topological Boundary States
• Abstract summary: A general plaquette chiral model in two dimensions serves as a minimal realization of dual weak topology.<n>The weak-topological edge states correspond to exceptional points in complex momentum space, while corner zero modes emerge from exceptional curves obtained by complexifying both momenta.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: In this article, we demonstrate that weak topology can be formulated geometrically in terms of exceptional singularities of an analytically continued Bloch Hamiltonian. A general plaquette chiral model in two dimensions serves as a minimal realization of dual weak topology, possessing two independent families of weak topological invariants, one for each spatial direction. The weak-topological edge states correspond to exceptional points in complex momentum space, while corner zero modes emerge from exceptional curves obtained by complexifying both momenta. Compact localized states arise when the exceptional roots collapse to the origin. This framework provides a unified complex-momentum description of edge, corner, and compact localization.

Related papers

• Temporal Entanglement from Twist Correlators in 2d Conformal Field Theory and Holography [36.94429692322632]
  We formulate timelike entanglement entropy and its Rényi extension in two-dimensional conformal field theory.<n>Within three-dimensional holography, the semiclassical boundary correlator identifies boundary-anchored complex geodesics as the relevant bulk saddles.<n>We develop these ideas in several representative settings, including locally and globally excited states and quantum operator quenches.
  arXiv  Detail & Related papers  (2026-07-15T16:40:45Z)
• Dynamics of Gradient Descent with Large Step Size Near a Manifold of Flat Minima [39.50927136881194]
  An important quantity in the theory of gradient descent (GD) is the emphsharpness, defined as the largest eigenvalue of the objective Hessian.<n>Recent work bridges this gap in the setting of overparametrised least-squares with a emphsingle scalar output<n>We show that our framework applies to deep matrix factorisation under mild assumptions, yielding several new structural results.
  arXiv  Detail & Related papers  (2026-07-09T11:58:44Z)
• Krylov complexity and fidelity susceptibility in two-band Hamiltonians [1.3066182802188202]
  We investigate Krylov spread complexity for the ground state of two-band Hamiltonians, where the reference state is a generic state on the Bloch sphere.<n>For generic reference states, the derivative of the spread complexity is logarithmically divergent at the topological phase transition in the Su-Schrieffer-Heeger model.
  arXiv  Detail & Related papers  (2026-05-18T16:07:09Z)
• Inverse Design of Strongly Localized Topological $π$ Modes in One-Dimensional Nonperiodic Systems [0.0]
  Inverse design of a potential sequence is performed using a generative model under a global topological constraint.<n>The generated sequence reveals a characteristic structure consisting of a topological boundary layer and a macroscopic S-dense domain.<n>Results provide a compact design principle for strongly localized topological states.
  arXiv  Detail & Related papers  (2026-03-31T14:45:08Z)
• Continuum field theory of matchgate tensor network ensembles [36.94429692322632]
  We develop a continuum description for random ensembles of two-dimensional fermionic matchgate tensor networks.<n>As a diagnostic of the resulting universal physics, we analyze disorder-averaged moments of fermionic two-point functions.<n>We show that disorder drives universal long-distance behavior governed by a nonlinear sigma-model of symmetry class D with a topological term.
  arXiv  Detail & Related papers  (2026-03-06T12:15:35Z)
• Chiral gapped states are universally non-topological [5.313708865591889]
  We show that corner entanglement in a 2+1D chiral gapped groundstate provides an obstruction to a gapped boundary.<n>One reward from our analysis is that we can construct a local gapped Hamiltonian within the same chiral gapped phase from a given wavefunction.<n>Our analysis of corner entanglement reveals the emergence of a universal conformal geometry encoded in the entanglement structure of bulk regions of chiral gapped states.
  arXiv  Detail & Related papers  (2025-10-27T18:00:20Z)
• Entanglement Spectrum Resolved by Loop Symmetries [0.0]
  A rigorous analysis is presented for the entanglement spectrum of quantum many-body states possessing a higher-form group-representation symmetry generated by topological Wilson loops.<n>In particular, it is shown for the Kitaev quantum double model that not only the topological entanglement entropy can be reproduced, but also the Li-Haldane conjecture concerning the full entanglement spectrum holds exactly.
  arXiv  Detail & Related papers  (2025-10-21T07:11:06Z)
• Observation of non-Hermitian bulk-boundary correspondence in non-chiral non-unitary quantum dynamics of single photons [31.05848822220465]
  In non-Hermitian systems, preserved chiral symmetry is one of the key ingredients, which plays a pivotal role in determining non-Hermitian topology.<n>We theoretically predict and experimentally demonstrate the bulk-boundary correspondence of a one-dimensional (1D) non-Hermitian system with chiral symmetry breaking.
  arXiv  Detail & Related papers  (2025-04-07T09:43:43Z)
• Topological nature of edge states for one-dimensional systems without symmetry protection [46.87902365052209]
  We numerically verify and analytically prove a winding number invariant that correctly predicts the number of edge states in one-dimensional, nearest-neighbor (between unit cells)<n>Our winding number is invariant under unitary or similarity transforms.
  arXiv  Detail & Related papers  (2024-12-13T19:44:54Z)
• Topological Order in the Spectral Riemann Surfaces of Non-Hermitian Systems [44.99833362998488]
  We show topologically ordered states in the complex-valued spectra of non-Hermitian systems.<n>These arise when the distinctive exceptional points in the energy surfaces of such models are annihilated.<n>We illustrate the characteristics of the topologically protected states in a non-Hermitian two-band model.
  arXiv  Detail & Related papers  (2024-10-24T10:16:47Z)
• Mixed-State Entanglement Measures in Topological Order [0.685316573653194]
  We study the entanglement in topologically ordered states between two arbitrary spatial regions. While the field-theoretic results are expected to be topological and universal, the lattice results contain nontopological/nonuniversal terms as well.
  arXiv  Detail & Related papers  (2023-01-19T17:59:50Z)

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.