Zoology of non-Hermitian spectra and their graph topology

Abstract

We uncover the very rich graph topology of generic bounded non-Hermitian spectra, distinct from the topology of conventional band invariants and complex spectral winding. The graph configuration of complex spectra are characterized by the algebraic structures of their corresponding energy dispersions, drawing new intimate links between combinatorial graph theory, algebraic geometry and non-Hermitian band topology. Spectral graphs that are conformally related belong to the same equivalence class, and are characterized by emergent symmetries not necessarily present in the physical Hamiltonian. The simplest class encompasses well-known examples such as the Hatano-Nelson and non-Hermitian SSH models, while more sophisticated classes represent novel multi-component models with interesting spectral graphs resembling stars, flowers, and insects. With recent rapid advancements in metamaterials, ultracold atomic lattices and quantum circuits, it is now feasible to not only experimentally realize such esoteric spectra, but also investigate the non-Hermitian flat bands and anomalous responses straddling transitions between different spectral graph topologies.

32 pages, 22 figures

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Cited by in corpus (24)

• Dimensional transmutation from non-Hermiticity
• Designing non-Hermitian real spectra through electrostatics
• Scale-tailored localization and its observation in non-Hermitian electrical circuits
• Occupation-dependent particle separation in one-dimensional non-Hermitian lattices
• Percolation-induced PT symmetry breaking
• Non-Hermitian Topology in Hermitian Topological Matter
• Exact Solutions Disentangle Higher-Order Topology in 2D Non-Hermitian Lattices
• Dynamical suppression of many-body non-Hermitian skin effect in Anyonic systems
• Braiding Topology of Non-Hermitian Open-Boundary Bands
• Observation of non-local impedance response in a passive electrical circuit
• Non-Hermitian Skin Effect Along Hyperbolic Geodesics
• Entangelment Entropy on Generalized Brillouin Zone
• Enhanced frequency and temperature estimation by a $\mathcal{P}\mathcal{T}$-symmetric quantum oscillator
• Nonlinear Hall effects with an exceptional ring
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• Many-body critical non-Hermitian skin effect
• Non-Hermitian dynamical topological winding in photonic mesh lattices
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• Non-Hermitian ultra-strong bosonic clustering through interaction-induced caging
• Tentaclelike spectra and bound states in Hatano-Nelson chain with long-range impurity coupling
• Topologically protected negative entanglement
• Experimentally Probing Non-Hermitian Spectral Transition and Eigenstate Skewness
• Topology of the generalized Brillouin zone of one-dimensional models
• Wiener-Hopf factorization and non-Hermitian topology for Amoeba formulation in one-dimensional multiband systems