Zak phase and bulk-boundary correspondence in a generalized Dirac–Kronig–Penney model
- 1Sapienza Università di Roma
- 2Aalborg University
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
- Quantum transmission in 1D disordered stealthy hyperuniform Kronig--Penney-like models
- Arithmetic triangular structures in the transfer-matrix of finite Kronig-Penney models
- Walk/Zeta correspondence for quantum walks on path graphs: a pre-geometric structure implied by a generalized reflection principle
- Bulk-Boundary Correspondence in Semi-Infinite Chains from Sublattice Zeros
- Interaction-Enabled Bulk-Boundary Correspondence without a Global Band Gap
BibTeX
@article{angelone2026phase,
title = {{Zak phase and bulk-boundary correspondence in a generalized Dirac–Kronig–Penney model}},
author = {Giuliano Angelone and Domenico Monaco and Gabriele Peluso},
journal = {New Journal of Physics},
year = {2026},
month = oct,
doi = {10.1088/1367-2630/aeb4e5},
url = {https://iopscience.iop.org/article/10.1088/1367-2630/aeb4e5},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - Zak phase and bulk-boundary correspondence in a generalized Dirac–Kronig–Penney model
AU - Giuliano Angelone
AU - Domenico Monaco
AU - Gabriele Peluso
PY - 2026
DA - 2026/10/29
JO - New Journal of Physics
DO - 10.1088/1367-2630/aeb4e5
UR - https://iopscience.iop.org/article/10.1088/1367-2630/aeb4e5
AB - 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.
SN - 1367-2630
ER -