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PreprintarXiv licencearXiv

Bulk-Boundary Correspondence in Semi-Infinite Chains from Sublattice Zeros

  • Ilya Iakoub
  • Nicolas Levasseur
  • Kylian Lionnet
  • Richard MacKenzie
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Abstract

We provide an alternative derivation of the bulk-boundary correspondence for semi-infinite chains. To describe edge states, we analytically continue the usual Bloch Hamiltonian to complex wave vectors k. To start, we note that the zeros of a Bloch wavefunction are related to edge states, at least in systems with nearest-neighbour hoppings. We show that an analytically continued Bloch Hamiltonian with chiral symmetry has exceptional points, where two different states coalesce. These special points are related to the adiabatic protection of edge states. We derive a winding number that counts the exceptional states which, together with the boundary conditions, give a lower bound on the number of edge states protected by chiral symmetry. This bound is saturated in the models we consider.

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Cite

BibTeXRIS
BibTeX
@misc{iakoub2026bulkboundary,
  title = {{Bulk-Boundary Correspondence in Semi-Infinite Chains from Sublattice Zeros}},
  author = {Ilya Iakoub and Nicolas Levasseur and Kylian Lionnet and Richard MacKenzie},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2608.01368},
  eprint = {2608.01368},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2608.01368},
}
RIS
TY  - UNPB
TI  - Bulk-Boundary Correspondence in Semi-Infinite Chains from Sublattice Zeros
AU  - Ilya Iakoub
AU  - Nicolas Levasseur
AU  - Kylian Lionnet
AU  - Richard MacKenzie
PY  - 2026
DA  - 2026/11/01
PB  - arXiv
DO  - 10.48550/arxiv.2608.01368
UR  - https://arxiv.org/abs/2608.01368
AB  - We provide an alternative derivation of the bulk-boundary correspondence for semi-infinite chains. To describe edge states, we analytically continue the usual Bloch Hamiltonian to complex wave vectors k. To start, we note that the zeros of a Bloch wavefunction are related to edge states, at least in systems with nearest-neighbour hoppings. We show that an analytically continued Bloch Hamiltonian with chiral symmetry has exceptional points, where two different states coalesce. These special points are related to the adiabatic protection of edge states. We derive a winding number that counts the exceptional states which, together with the boundary conditions, give a lower bound on the number of edge states protected by chiral symmetry. This bound is saturated in the models we consider.
ER  -