Zak phase and bulk-boundary correspondence in a generalized Dirac-Kronig-Penney model

• URL: http://arxiv.org/abs/2602.03378v1
• Date: Tue, 03 Feb 2026 10:56:57 GMT
• Title: Zak phase and bulk-boundary correspondence in a generalized Dirac-Kronig-Penney model
• Authors: Giuliano Angelone, Domenico Monaco, Gabriele Peluso,
• Abstract summary: We investigate the topological properties of a continuum one-dimensional model for a relativistic quantum chain.<n>By tuning the coupling parameters this model can accommodate five Altland--Zirnbauer--Cartan symmetry classes.<n>We numerically compute the Zak phase to probe the bulk topological content of the insulating phases.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We investigate the topological properties of a generalized Dirac--Kronig--Penney model, a continuum one-dimensional model for a relativistic quantum chain. By tuning the coupling parameters this model can accommodate five Altland--Zirnbauer--Cartan symmetry classes, three of which (AIII, BDI and D) support non-trivial topological phases in dimension one. We characterize analytically the spectral properties of the Hamiltonian in terms of a spectral function, and numerically compute the Zak phase to probe the bulk topological content of the insulating phases. Our findings reveal that, while the Zak phase is quantized in classes AIII and BDI, it exhibits non-quantized values in class D, challenging its traditional role as a topological marker in continuum settings. We also discuss the bulk-boundary correspondence for a truncated version of the chain, analyzing how the emergence of edge states depends on both the truncation position and the boundary conditions. In classes AIII and BDI, we find that the Zak phase effectively detects edge states as a relative boundary topological index, although the correspondence is highly sensitive to the parameters characterizing the truncation.

Related papers

• Wilson Line and Disorder Invariants of Topological One-Dimensional Multiband Models [0.0]
  Topological invariants, such as the winding number, the Chern number, and the Zak phase, characterize the topological phases of bulk materials.<n>We introduce the unwrapped Wilson line across the Brillouin zone to compute the bulk topological invariant.<n>This approach accurately captures all topological edge states, including those overlooked by traditional invariants.
  arXiv  Detail & Related papers  (2025-07-02T15:59:44Z)
• Nonlinearity-driven Topology via Spontaneous Symmetry Breaking [79.16635054977068]
  We consider a chain of parametrically-driven quantum resonators coupled only via weak nearest-neighbour cross-Kerr interaction.<n>Topology is dictated by the structure of the Kerr nonlinearity, yielding a non-trivial bulk-boundary correspondence.
  arXiv  Detail & Related papers  (2025-03-15T00:20:45Z)
• Quantum entanglement of fermionic symmetry-enriched quantum critical points in one dimension [0.0]
  We show that two transition lines exhibit fundamentally different topological properties despite sharing the same central charge.<n>We also identify a novel Lifshitz multicritical point at the intersection of the three transition lines.<n>This work provides a valuable reference for investigating gapless topological phases of matter from the perspective of quantum entanglement.
  arXiv  Detail & Related papers  (2025-02-25T13:11:34Z)
• Topology and Spectrum in Measurement-Induced Phase Transitions [0.0]
  We propose a general framework based on Lyapunov analysis to characterize topological properties in monitored quantum systems.<n>We illustrate this framework by analyzing (1+1)-dimensional monitored circuits for Majorana fermions.
  arXiv  Detail & Related papers  (2024-12-15T07:32:16Z)
• Two-dimensional symmetry-protected topological phases and transitions in open quantum systems [0.07673339435080445]
  We investigate the influence of local decoherence on a symmetry-protected topological SPT phase of the two-dimensional (2D) cluster state. We show a topological phase transition of a $mathbbZ(0)timesmathbbZ_2(1)$ SPT phase into the trivial phase occurring at a finite decoherence strength.
  arXiv  Detail & Related papers  (2023-11-21T14:05:48Z)
• Softening of Majorana edge states by long-range couplings [77.34726150561087]
  Long-range couplings in the Kitaev chain is shown to modify the universal scaling of topological states close to the critical point. We prove that the Majorana states become increasingly delocalised at a universal rate which is only determined by the interaction range.
  arXiv  Detail & Related papers  (2023-01-29T19:00:08Z)
• Experimental Observation of Topological Quantum Criticality [47.187609203210705]
  We report on the observation of quantum criticality forming at the transition point between topological Anderson insulator phases in a one-dimensional photonic quantum walk with spin. The walker's probability distribution reveals a time-staggered profile of the dynamical spin-susceptibility.
  arXiv  Detail & Related papers  (2023-01-13T08:04:20Z)
• Topological transitions with continuously monitored free fermions [68.8204255655161]
  We show the presence of a topological phase transition that is of a different universality class than that observed in stroboscopic projective circuits. We find that this entanglement transition is well identified by a combination of the bipartite entanglement entropy and the topological entanglement entropy.
  arXiv  Detail & Related papers  (2021-12-17T22:01:54Z)
• Boundary theories of critical matchgate tensor networks [59.433172590351234]
  Key aspects of the AdS/CFT correspondence can be captured in terms of tensor network models on hyperbolic lattices. For tensors fulfilling the matchgate constraint, these have previously been shown to produce disordered boundary states. We show that these Hamiltonians exhibit multi-scale quasiperiodic symmetries captured by an analytical toy model.
  arXiv  Detail & Related papers  (2021-10-06T18:00:03Z)
• Scaling behavior in a multicritical one-dimensional topological insulator [0.0]
  We study a topological quantum phase transition with a second-order nonanalyticity of the ground-state energy. We find that the critical exponents and scaling law defined with respect to the spectral gap remain the same regardless of the order of the transition.
  arXiv  Detail & Related papers  (2020-08-18T21:05:14Z)
• 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)

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.