{
  "abstract": "Non-Bloch band theory recovers the open-boundary spectrum of a non-Hermitian chain from its Bloch Hamiltonian evaluated along the generalised Brillouin zone rather than the unit circle. We develop its finite-size counterpart for banded Toeplitz matrices with real open-boundary spectrum. Reality of the spectrum forces the generalised Brillouin zone to be parametrised by an analytic polar curve, so the known sufficient condition for a real spectrum is also necessary under some mild non-degeneracy conditions. At finite size $n$, the eigenvalues of the original and the symmetrised Bloch Hamiltonians are given by samples at $n$ quantised momenta from the same limiting band, although separated by a phase mismatch of order $1/n$ which we obtain in closed form. Iterating this correction $K$ times yields a quantisation rule on the generalised Brillouin zone reproducing the finite spectrum with an error $\\mathcal{O}(n^{-K-1})$ for any fixed $K$. At finite size, the generalised Brillouin zone itself is unchanged and only its parametrisation depends on $n$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.13715",
  "author_total": 2,
  "authors": [
    {
      "name": "Yannick de Bruijn"
    },
    {
      "name": "Erik Orvehed Hiltunen"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9a2b0h1wqc03f.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.13715",
  "fulltext_url": null,
  "id": "9a2b0h1wqc03f",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.13715",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.SP"
    ],
    [
      "openalex",
      "3107|Quantum Mechanics and Non-Hermitian Physics"
    ]
  ],
  "openalex": "W7221527612",
  "pdf_url": "https://arxiv.org/pdf/2610.13715",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-09",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9a2b0h1wqc03f.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:28:40Z",
      "native_id": "2610.13715",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.13715"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.SP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Non-Bloch band theory for finite banded non-Hermitian Toeplitz matrices",
  "title_text": "Non-Bloch band theory for finite banded non-Hermitian Toeplitz matrices",
  "type": "preprint",
  "updated_at": "2026-10-30T12:28:40Z",
  "url": "https://research.draconitic.com/paper/9a2b0h1wqc03f",
  "venue": "arXiv",
  "versions": []
}