Universal aspects of bulk density of states in non-Hermitian lattices

[2608.14508] Universal aspects of bulk density of states in non-Hermitian lattices Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Condensed Matter > Mesoscale and Nanoscale Physics arXiv:2608.14508 (cond-mat) [Submitted on 14 Aug 2026] Title: Universal aspects of bulk density of states in non-Hermitian lattices Authors: Mykhailo Pavliuk , Askar Iliasov , Emil J. Bergholtz , Tomáš Bzdušek View a PDF of the paper titled Universal aspects of bulk density of states in non-Hermitian lattices, by Mykhailo Pavliuk and 3 other authors View PDF HTML (experimental) Abstract: Non-Hermitian lattice Hamiltonians generally exhibit strong boundary sensitivity, with periodic and open boundary conditions producing distinct density of states (DOS) in the complex-energy plane. This has led to the view that extended non-Hermitian systems lack a unique bulk DOS, with different prescriptions representing inequivalent bulk physics. Here, we show that this apparent ambiguity is largely illusory. For any finite-range tight-binding Hamiltonian, we establish a universal bulk structure: all DOS definitions arising as thermodynamic limits of finite systems share identical multipole moments and generate identical bulk dynamics at finite times and for observables measured far from boundaries. This universality is intimately tied to the thermodynamic Green's functions, which we show to be independent of the boundary condition for large enough complex frequencies. Among all equivalent descriptions, we identify the Brown measure - obtained via Hermitization and resolvent analysis - as a canonical and convenient representative of the bulk DOS, defined directly from the infinite-volume Hamiltonian. We further show that point-gap topology imposes additional universal constraints: boundary-dependent Green's functions are forced to coincide throughout topologically trivial point gaps. This, in particular, provides a systematic criterion, valid in arbitrary dimension, for determining where and how eigenvalues of different boundary truncations can accumulate in the complex plane, and precisely delineates the regime in which the DOS ambiguity retains physical significance. Comments: 17 pages, 8 figures Subjects: Mesoscale and Nanoscale Physics (cond-mat.mes-hall) ; Quantum Physics (quant-ph) Cite as: arXiv:2608.14508 [cond-mat.mes-hall] (or arXiv:2608.14508v1 [cond-mat.mes-hall] for this version) https://doi.org/10.48550/arXiv.2608.14508 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Mykhailo Pavliuk [ view email ] [v1] Fri, 14 Aug 2026 17:22:43 UTC (689 KB) Full-text links: Access Paper: View a PDF of the paper titled Universal aspects of bulk density of states in non-Hermitian lattices, by Mykhailo Pavliuk and 3 other authors View PDF HTML (experimental) TeX Source view license Current browse context: cond-mat.mes-hall < prev | next > new | recent | 2026-08 Change to browse by: cond-mat quant-ph References & Citations INSPIRE HEP NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... 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