Non-Hermitian systems and topology: A transfer-matrix perspective

2018/12/31 by Flore K. Kunst, Vatsal Dwivedi · 1 citation
Mathematics · Physics and Astronomy · #Biorthogonal system #Boundary (topology) #Boundary value problem #Combinatorics #Computer science #Hermitian matrix #Invariant (physics) #Materials science #Mathematical analysis #Mathematical physics #Mathematics #Matrix (chemical analysis) #Nonlinear Photonic Systems #Physics #Pure mathematics #Quantum Mechanics and Non-Hermitian Physics #Topological Materials and Phenomena #Topology (electrical circuits) #cond-mat.mes-hall #quant-ph

paper · pdf · doi:10.1103/physrevb.99.245116

published as Phys. Rev. B 99, 245116 (2019)

openalex publication_date 2019/06/10 · arxiv created 2019/06/28 · arxiv updated 2019/07/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06

Abstract

Non-Hermitian Hamiltonians---proposed to describe dissipative systems where the particles have a finite lifetime---exhibit many puzzling properties, strongly contrasting their Hermitian counterparts. In particular, their spectra exhibit extreme sensitivity to boundary conditions and a piling up of all states at the boundary, signalling a breakdown of the conventional bulk-boundary correspondence. The authors study these systems using transfer matrices, whereby they can explain as well as predict the aforementioned features without resorting to numerical computations. This analytical approach allows for a deeper understanding of the topological properties of non-Hermitian systems.

Citations

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Cited by

• Non-Hermitian Pseudo-Gaps
• Non-Bloch band theory and bulk–edge correspondence in non-Hermitian systems