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Non-Bloch Band Theory of Non-Hermitian Systems

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arxiv 1902.10958 v2 pith:KU3C6HUB submitted 2019-02-28 cond-mat.mes-hall

Kazuki Yokomizo , Shuichi Murakami This is my paper · ORCID
classification cond-mat.mes-hall
keywords bandsystemstheorynon-hermitianblochbrillouinopenperiodic
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In spatially periodic Hermitian systems, such as electronic systems in crystals, the band structure is described by the band theory in terms of the Bloch wave functions, which reproduce energy levels for large systems with open boundaries. In this paper, we establish a generalized Bloch band theory in one-dimensional spatially periodic tight-binding models. We show how to define the Brillouin zone in non-Hermitian systems. From this Brillouin zone, one can calculate continuum bands, which reproduce the band structure in an open chain. As an example, we apply our theory to the non-Hermitian Su-Schrieffer-Heeger model. We also show the bulk-edge correspondence between the winding number and existence of the topological edge states.

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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Non-Hermitian Quantum Adiabatic Algorithm

    quant-ph 2026-07 conditional novelty 7.0 of 10

    A history-decoupled Hamiltonian mapping makes non-Hermitian adiabatic quantum optimization pseudospectrally stable, achieving polynomial-time (per configuration) evolution on the CK maximum-independent-set benchmarks.

  2. Extracting Boundary Conformal Data from Periodic Non-Hermitian Critical Chains

    cond-mat.stat-mech 2026-06 conditional novelty 7.0 of 10

    Periodic-chain projected overlaps with paired left duals extract universal boundary CFT coefficients, including a negative Yang-Lee ratio and complex Potts boundary data.

  3. Entanglement spectrum and symmetries in non-Hermitian fermionic non-interacting models

    cond-mat.mes-hall 2019-08 conditional novelty 6.0 of 10

    Non-Hermitian free-fermion entanglement spectra can be computed efficiently, and the biorthogonal entanglement Hamiltonian reproduces bulk topology in line-gapped phases.

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