2023/11/25 by Yuncheng Xiong, Haiping Hu, Xiong, Yuncheng +1 · 4 citations
Engineering · Physics and Astronomy · #Advanced Fiber Laser Technologies #Combustion and Detonation Processes #FOS: Physical sciences #Mathematical Physics (math-ph) #Mesoscale and Nanoscale Physics (cond-mat.mes-hall) #Optics (physics.optics) #Quantum Gases (cond-mat.quant-gas) #Quantum Mechanics and Non-Hermitian Physics #Quantum Physics (quant-ph)
paper · pdf · doi:10.48550/arxiv.2311.14921
openalex publication_date 2023/11/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Non-Hermitian systems exhibit diverse graph patterns of energy spectra under open boundary conditions. Here we present an algebraic framework to comprehensively characterize the spectral geometry and graph topology of non-Bloch bands. Using a locally defined potential function, we unravel the spectral-collapse mechanism from Bloch to non-Bloch bands, delicately placing the spectral graph at the troughs of the potential landscape. The potential formalism deduces non-Bloch band theory and generates the density of states via Poisson equation. We further investigate the Euler-graph topology by classifying spectral vertices based on their multiplicities and projections onto the generalized Brillouin zone. Through concrete models, we identify three elementary graph-topology transitions (UVY, PT-like, and self-crossing), accompanied by the emergence of singularities in the generalized Brillouin zone. Lastly, we unveil how to generally account for isolated edge states outside the spectral graph. Our work lays the cornerstone for exploring the versatile spectral geometry and graph topology of non-Hermitian non-Bloch bands.