Wiener-Hopf factorization and non-Hermitian topology for Amoeba formulation in one-dimensional multiband systems

Abstract

The non-Hermitian skin effect (NHSE), characterized by the extensive localization of bulk modes at the boundaries, has attracted significant attention as a hallmark feature of non-Hermitian topology. This localization invalidates the conventional Bloch band theory, necessitating an analysis under open boundary conditions even in the thermodynamic limit. The Amoeba formulation addresses this challenge by computing the spectral potential rather than the spectrum itself. Based on the (strong) Szegö limit theorem and its topological generalization, this approach reduces the evaluation of the potential to an optimization problem involving the Ronkin function. However, while the generalized Szegö limit theorem is formally applicable in arbitrary dimensions, its implementation is limited to single-band systems, and its applicability to multiband systems remains unclear even in one-dimensional systems. In this paper, we establish the Wiener-Hopf factorization (WHF) of the non-Bloch Hamiltonian as a powerful framework, providing a unified and rigorous foundation for Amoeba analysis in one-dimensional multiband systems. By combining the WHF with Hermitian doubling, we first elucidate the applicability criteria for the generalized Szegö limit theorem in multiband systems. We then show that the WHF provides the natural mathematical origin for the symmetry-decomposed Ronkin function in symmetry class AII${}^{†}$, leading to a rigorous proof of the generalized Szegö limit theorem for these systems and opening a path toward systematic generalizations to other symmetry classes.

arXiv comment24 pages, 15 figures

References in corpus (76)

• Edge states and topological invariants of non-Hermitian systems
• Exceptional Topology of Non-Hermitian Systems
• Non-Hermitian Physics
• Topological phases of non-Hermitian systems
• Symmetry and Topology in Non-Hermitian Physics
• Biorthogonal Bulk-Boundary Correspondence in Non-Hermitian Systems
• Topological Origin of Non-Hermitian Skin Effects
• Non-Bloch Band Theory of Non-Hermitian Systems
• Correspondence between winding numbers and skin modes in non-hermitian systems
• Observation of bulk boundary correspondence breakdown in topolectrical circuits
• Non-Hermitian Boundary Modes
• Observation of non-Hermitian bulk-boundary correspondence in quantum dynamics
• Efficient Light Funneling based on the non-Hermitian Skin Effect
• Anatomy of skin modes and topology in non-Hermitian systems
• Non-Hermitian robust edge states in one-dimension: Anomalous localization and eigenspace condensation at exceptional points
• Non-Hermitian Topology and Exceptional-Point Geometries
• Observation of non-Hermitian topology and its bulk-edge correspondence in an active mechanical metamaterial
• Non-Hermitian bulk-boundary correspondence and auxiliary generalized Brillouin zone theory
• Non-reciprocal robotic metamaterials
• Hybrid higher-order skin-topological modes in non-reciprocal systems
• Second-Order Topological Phases in Non-Hermitian Systems
• Non-Hermitian Topological Invariants in Real Space
• Critical non-Hermitian Skin Effect
• Reciprocal skin effect and its realization in a topolectrical circuit
• Observation of Non-Hermitian Skin Effect and Topology in Ultracold Atoms
• Higher-order non-Hermitian skin effect
• Observation of higher-order non-Hermitian skin effect
• Tunable non-reciprocal quantum transport through a dissipative Aharonov-Bohm ring in ultracold atoms
• Non-Bloch band theory of non-Hermitian Hamiltonians in the symplectic class
• Entanglement Phase Transition Induced by the Non-Hermitian Skin Effect
• Non-Hermitian systems and topology: A transfer-matrix perspective
• Knots and Non-Hermitian Bloch Bands
• Perspective on topological states of non-Hermitian lattices
• Non-Bloch band collapse and chiral Zener tunneling
• Transient non-Hermitian skin effect
• Simple formulas of directional amplification from non-Bloch band theory
• Mirror skin effect and its electric circuit simulation
• Guided accumulation of active particles by topological design of a second-order skin effect
• Topological Field Theory of Non-Hermitian Systems
• Amoeba Formulation of Non-Bloch Band Theory in Arbitrary Dimensions
• Inner Skin Effects on Non-Hermitian Topological Fractals
• Quantum anomaly, non-Hermitian skin effects, and entanglement entropy in open systems
• Non-Hermitian skin effect and self-acceleration
• Non-Bloch band theory in bosonic Bogoliubov-de Gennes systems
• Enhancement of Second-Order Non-Hermitian Skin Effect by Magnetic Fields
• Non-Bloch bands in two-dimensional non-Hermitian systems
• Dimensional transmutation from non-Hermiticity
• Hermitian zero modes protected by nonnormality: Application of pseudospectra
• Geometric Origin of Non-Bloch PT Symmetry Breaking
• Non-Hermitian band topology with generalized inversion symmetry
• Zoology of non-Hermitian spectra and their graph topology
• Topological origin of non-Hermitian skin effect in higher dimensions and uniform spectra
• Observation of the non-Hermitian skin effect and Fermi skin on a digital quantum computer
• Bulk-boundary correspondence in point-gap topological phases
• Topological energy braiding of the non-Bloch bands
• Non-Bloch quench dynamics
• Topological enhancement of non-normality in non-Hermitian skin effects
• A brief review of hybrid skin-topological effect
• Edge theory of non-Hermitian skin modes in higher dimensions
• Green's functions of multiband non-Hermitian systems
• Non-Bloch band theory for non-Hermitian continuum systems
• Modified Generalized-Brillouin-Zone Theory with On-site Disorders
• Exact Solutions Disentangle Higher-Order Topology in 2D Non-Hermitian Lattices
• Exact formulas of the end-to-end Green's functions in non-Hermitian systems
• Algebraic non-Hermitian skin effect and generalized Fermi surface formula in arbitrary dimensions
• Braiding Topology of Non-Hermitian Open-Boundary Bands
• Observation of non-local impedance response in a passive electrical circuit
• Constraints of internal symmetry on the non-Hermitian skin effect and bidirectional skin effect under the action of the Hermitian conjugate of time-reversal symmetry
• Modified Szego-Widom Asymptotics for Block Toeplitz Matrices with Zero Modes
• Tailoring Bound State Geometry in High-Dimensional Non-Hermitian Systems
• General theory for infernal points in non-Hermitian systems
• Entangelment Entropy on Generalized Brillouin Zone
• Topological characterization of a non-Hermitian ladder via Floquet non-Bloch theory
• Non-Bloch band theory for time-modulated discrete mechanical systems
• Non-Hermitian ${\mathbb{Z}}_4$ skin effect protected by glide symmetry
• Floquet Non-Bloch Formalism for a Non-Hermitian Ladder: From Theoretical Framework to Topolectrical Circuits