Non-Bloch Band Theory of Non-Hermitian Systems

Abstract

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.

15 pages, 8 figures

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• Engineering Dissipative Quasicrystals
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• Green's functions of multiband non-Hermitian systems
• Degeneracy and defectiveness in non-Hermitian systems with open boundary
• Point-gap topology with complete bulk-boundary correspondence in dissipative quantum systems
• Absence of logarithmic and algebraic scaling entanglement phases due to skin effect
• Universal scalefree non-Hermitian skin effect near the Bloch point
• Two-dimensional quantum walk with non-Hermitian skin effects
• Observation of a topological edge state stabilized by dissipation
• Phase transitions and bunching of correlated particles in a non-Hermitian quasicrystal
• Non-Hermitian Topology in Hermitian Topological Matter
• Absence of measurement-induced entanglement transition due to feedback-induced skin effect
• Non-Hermitian skin effect induced by Rashba-Dresselhaus spin-orbit coupling
• Anderson Delocalization in Strongly Coupled Disordered Non-Hermitian Chains
• The non-Hermitian skin effect: A perspective
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• General criterion for non-Hermitian skin effects and Application: Fock space skin effects in many body systems
• Generalized Bloch band theory for non-Hermitian bulk-boundary correspondence
• Irrational Non-Abelian Statistics for Non-Hermitian Generalization of Majorana Zero Modes
• Non-Hermitian Skin Effect in Periodically-Driven Dissipative Ultracold Atoms
• Self acceleration from spectral geometry in dissipative quantum-walk dynamics
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• Hybrid scale-free skin effect in non-Hermitian systems: A transfer matrix approach
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• Topological Phase Transitions of Generalized Brillouin Zone
• Non-linear dynamics of the non-Hermitian Su-Schrieffer-Heeger model
• Asymmetric transfer matrix analysis of Lyapunov exponents in one-dimensional non-reciprocal quasicrystals
• Emergent strength-dependent scale-free mobility edge in a non-reciprocal long-range Aubry-André-Harper model
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• Non-normal Hamiltonian dynamics in quantum systems and its realization on quantum computers
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• Anomalous Andreev Spectrum and Transport in Non-Hermitian Josephson Junctions
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• Quantum walks of correlated photons in non-Hermitian photonic lattices
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• Observation of Impurity-Induced Scale-Free Localization in a Disordered Non-Hermitian Electrical Circuit
• Observation of non-local impedance response in a passive electrical circuit
• Unravelling the edge spectra of non-Hermitian Chern insulators
• Non-Bloch PT symmetry breaking: Universal threshold and dimensional surprise
• Nontrivial worldline winding in non-Hermitian quantum systems
• Generalized Fermion Doubling Theorems: Classification of 2D Nodal Systems in Terms of Wallpaper Groups
• Hermitian Topologies originating from non-Hermitian braidings
• Bulk-edge correspondence with generalized chiral symmetry
• State-dependent Topological Invariants and Anomalous Bulk-Boundary Correspondence in non-Hermitian Topological Systems
• 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
• Quantum-Classical Correspondence of Non-Hermitian Symmetry Breaking
• Multifractality of many-body non-Hermitian skin effect
• Direct observation of energy band attraction effect in non-Hermitian systems
• Quantum metric dependent anomalous velocity in systems subject to complex electric fields
• Imaginary gap-closed points and dynamics in a class of dissipative systems
• Selective and tunable excitation of topological non-Hermitian skin modes
• Universal quantum Fisher information and simultaneous occurrence of Landau-class and topological-class transitions in non-Hermitian Jaynes-Cummings models
• Hopf Bifurcation of Nonlinear Non-Hermitian Skin Effect
• Role of Topology in Relaxation of One-Dimensional Stochastic Processes
• Entanglement transitions in a periodically driven non-Hermitian Ising chain
• Hermitian chiral boundary states in non-Hermitian topological insulators
• Fundamental constraints on the observability of non-Hermitian effects in passive systems
• Symmetry-Protected Topological Phase for Spin-Tensor-Momentum-Coupled Ultracold Atoms
• Investigation of a non-Hermitian edge burst with time-dependent perturbation theory
• Non-Hermitian boost deformation
• Exceptional points and non-Hermitian skin effects under nonlinearity of eigenvalues
• Non-Hermitian skin effect enforced by nonsymmorphic symmetries
• Extended imaginary gauge transformation in a general nonreciprocal lattice
• Discriminant indicators with generalized inversion symmetry
• Extrinsic Mechanisms of Phonon Magnetic Moment
• Information constraint in open quantum systems
• A symmetry-protected exceptional ring in a photonic crystal with negative index media
• Andreev non-Hermitian Hamiltonian for open Josephson junctions from Green's functions
• Complex semiclassical theory for non-Hermitian quantum systems
• Non-Hermitian three-dimensional two-band Hopf insulator
• Biorthogonal topological charge pumping in non-Hermitian systems
• Relationship between the Electronic Polarization and the Winding Number in Non-Hermitian Systems
• Detecting bulk and edge exceptional points in non-Hermitian systems through generalized Petermann factors
• Equivalence and superposition of real and imaginary quasiperiodicities
• Fate of non-Hermitian free fermions with Wannier-Stark ladder
• Versatile Control of Nonlinear Topological States in Non-Hermitian Systems
• Generalized Lieb's theorem for noninteracting non-Hermitian $n$-partite tight-binding lattices
• Numerical instability of non-Hermitian Hamiltonian evolutions
• Effective impurity behavior emergent from non-Hermitian proximity effect
• Non-Hermitian Quantum Fractals
• Dynamical signatures of the Yang-Lee edge singularity in non-Hermitian systems
• Tailoring Bound State Geometry in High-Dimensional Non-Hermitian Systems
• Universal spectral moment theorem and its applications in non-Hermitian systems
• Hilbert space fragmentation imposed real spectrum of non-Hermitian systems
• Bulk-Edge Correspondence for Point-Gap Topological Phases in Junction Systems
• Interaction-Induced Second-Order Skin Effect
• Scale-free localization versus Anderson localization in unidirectional quasiperiodic lattices
• Non-Hermitian skin effect in a single trapped ion
• Quantum quenches in a pseudo-Hermitian Chern insulator
• Skin Effect Induced Anomalous Dynamics from Charge-Fluctuating Initial States
• Eigenstate clustering around exceptional points
• Anomalous pumping in the non-Hermitian Rice-Mele model
• Edge states in a non-Hermitian topological crystalline insulator
• Non-Floquet engineering in periodically driven non-Hermitian systems
• Quasiperiodicity-induced bulk localization with self similarity in non-Hermitian systems
• Topological indicators for systems with open boundaries: Application to the Kitaev wire
• Non-Hermitian semi-Dirac semi-metals
• Unconventional and robust light-matter interactions based on the non-Hermitian skin effect
• Localization and topological transitions in generalized non-Hermitian SSH models
• Entangelment Entropy on Generalized Brillouin Zone
• General theory for infernal points in non-Hermitian systems
• Quantum circuit for measuring an operator's generalized expectation values and its applications to non-Hermitian winding numbers
• Unprotected edge modes in quantum spin Hall insulator candidate materials
• Visualizing Topology of Real-Energy Gapless Phase Arising from Exceptional Point
• Non-Hermitian superconducting diode effect
• Real spectra in one-dimensional single-band non-Hermitian Hamiltonians
• Defective Edge states and Anomalous Bulk-boundary Correspondence for Topological Insulators under Non-Hermitian Similarity Transformation
• Emergent $\mathcal{P}\mathcal{T}$-symmetry breaking of collective modes with topological critical phenomena
• Intrinsic-perturbation induced anomalous higher-order boundary states in non-Hermitian systems
• Coexistence of non-Hermitian skin effect and extended states in one-dimensional nonreciprocal lattices
• Non-Bloch dynamics and topology in a classical non-equilibrium process
• Localization and mobility edges in non-Hermitian continuous quasiperiodic systems
• Competing topological phases in a non-Hermitian time-reversal symmetry-broken Bernevig-Hughes-Zhang model
• Chiral-Extended Photon-Emitter Dressed States in Non-Hermitian Topological Baths
• Controlled probing of localization effects in the non-Hermitian Aubry-André model via topolectrical circuits
• Non-Hermitian physics of levitated nanoparticle array
• Exceptional magic angles in non-Hermitian twisted bilayer graphene
• Non-Hermitian skin effect and lasing of absorbing open-boundary modes in photonic crystals
• Topological characterization of a non-Hermitian ladder via Floquet non-Bloch theory
• $\mathcal{P}\mathcal{T}$ symmetry of a square-wave modulated two-level system
• Non-Bloch Dirac Points and Phase Diagram in the Stacked Non-Hermitian SSH Model
• The Quantum Skin Hall Effect
• Anisotropic-scaling localization in higher-dimensional non-Hermitian systems
• Non-Hermitian tuned topological band gap
• Anomalous hybridization of spectral winding topology in quantized steady-state responses
• Non-Hermitian entanglement dip from scaling-induced exceptional criticality
• Observation of non-Hermitian many-body skin effects in Hilbert space
• Delocalization of skin steady states
• Non-Bloch band theory for time-modulated discrete mechanical systems
• Dissipative two-dimensional Raman lattice
• Generalized topological bulk-edge correspondence in bulk-Hermitian continuous systems with non-Hermitian boundary conditions
• Many-Body Non-Hermitian Skin Effect with Exact Steady States in the Dissipative Quantum Link Model
• Abnormal Frequency Response Determined by Saddle Points in Non-Hermitian Crystal Systems
• Complex entanglement entropy for complex conformal field theory
• Electronic polarization in non-Bloch band theory
• Quasi-stationary solutions in non-Hermitian systems
• Emergent localized states at the interface of a twofold $\mathcal{P}\mathcal{T}$-symmetric lattice
• Non-Bloch Theory for Spatiotemporal Photonic Crystals Assisted by Continuum Effective Medium
• Formal Green's function theory in non-Hermitian lattice systems
• Dissipation Enhanced Unidirectional Transport in Topological Systems
• Berry curvature inside parity-time-symmetry protected exceptional surface
• Topological Invariant for Multi-Band Non-hermitian Systems with Chiral Symmetry
• Inner non-Hermitian skin effect on Bethe lattice
• Nonlinear Hall effects with an exceptional ring
• Topological directed amplification
• Loss-induced universal one-way transport in periodically driven systems
• Super-enhanced Sensitivity in Non-Hermitian Systems at Infernal Points
• Real-time edge dynamics of non-Hermitian lattices
• Unconventional quantum criticality in a non-Hermitian extended Kitaev chain
• One-dimensional non-Hermitian band structures as Riemann surfaces
• Two-dimensional lattice with an imaginary magnetic field
• Topologically compatible non-Hermitian skin effect
• Optical pumping through the Liouvillian skin effect
• Machine learning of mirror skin effects in the presence of disorder
• Liouvillian skin effect in quantum neural networks
• Topology of Discrete Quantum Feedback Control
• Measuring Non-Hermitian Topological Invariants Directly from Quench Dynamics
• Restoration of non-Hermitian bulk-boundary correspondence by counterbalancing skin effect
• Inverse Design of Winding Tuple for Non-Hermitian Topological Edge Modes
• Fidelity and criticality in the nonreciprocal Aubry-Andr{é}-Harper model
• $K$-theory classification of Wannier localizability and detachable topological boundary states
• Tentaclelike spectra and bound states in Hatano-Nelson chain with long-range impurity coupling
• Exact solutions of non-Hermitian chains with asymmetric long-range hopping under specific boundary conditions
• Duality between Generalized Non-Hermitian HN Model in Flat Space and Hermitian System in Curved space
• Theory for the spectral splitting exponent of exceptional points
• Optical non-Hermitian skin effect in two-dimensional uniform media
• Model non-Hermitian topological operators without skin effect: A general principle of construction
• Distinguishability Transitions in Non-Unitary Boson Sampling Dynamics
• Topology and its detection in a dissipative Aharonov-Bohm chain
• Quantum Pontus-Mpemba Effect Enabled by the Liouvillian Skin Effect
• Delocalization of interacting directed polymers on a periodic substrate: Localization length and critical exponents from non-Hermitian spectra
• Non-Hermitian skin effect in fragmented Hilbert spaces of one-dimensional fermionic lattices
• Dual Symmetry Classification of Non-Hermitian Systems and ${\mathbb{Z}}_2$ Point-Gap Topology of a Non-Unitary Quantum Walk
• Winding Topology of Multifold Exceptional Points
• Entanglement Spectrum Dynamics as a Probe for Non-Hermitian Bulk-Boundary Correspondence in Systems with Periodic Boundaries
• Bulk-boundary correspondence in topological systems with the momentum dependent energy shift
• Impurity in a Fermi gas under non-Hermitian spin-orbit coupling
• General corner charge formulas in various tetrahedral and cubic space groups
• Quantized electrical, thermal, and spin transports of non-Hermitian clean and dirty two-dimensional topological insulators and superconductors
• Mobility rings in a non-Hermitian non-Abelian quasiperiodic lattice
• Renormalization approach to the analysis and design of Hermitian and non-Hermitian interfaces
• Exceptional second-order topological insulators
• Unveiling Non-Hermitian Spectral Topology in Hyperbolic Lattices with Non-Abelian Translation Symmetry
• Non-Hermitian ${\mathbb{Z}}_4$ skin effect protected by glide symmetry
• Hinge non-Hermitian skin effect in the single-particle properties of a strongly correlated f-electron system
• Band structures under non-Hermitian periodic potentials: Connecting nearly-free and bi-orthogonal tight-binding models
• Exact multiple complex mobility edges and quantum state engineering in coupled 1D quasicystals
• Exceptional deficiency of non-Hermitian systems
• Topological extension including quantum jump
• Fermi polaron in a dissipative bath with spin-orbit coupling
• Topological analysis of the complex SSH model using the quantum geometric tensor
• Dissolution of the non-Hermitian skin effect in one-dimensional lattices with linearly varying nonreciprocal hopping
• Topologically protected negative entanglement
• Coalescing hardcore-boson condensate states with nonzero momentum
• Bulk--Boundary Correspondence and Boundary Zero Modes in a Non-Hermitian Kitaev Chain Model
• Magnetization in a non-equilibrium quantum spin system
• Characterizing topological pumping of charges in exactly solvable Rice-Mele chains of the non-Hermitian variety
• Non-Hermitian Delocalization Induced by Residue Imaginary Velocity
• Phase Diagram of a Non-Hermitian Chern Insulator: Destabilization of Chiral Edge States and Bulk-Boundary Correspondence
• Hermitian and non-Hermitian topology in active matter
• Unifying Anderson transitions and topological amplification in non-Hermitian chains
• PT-symmetric Non-Hermitian Hopf Metal
• Uncovering Exceptional Contours in non-Hermitian Hyperbolic Matter
• Experimental observation of energy-band Riemann surface
• Coherent transfer of topological domain walls
• Concurrent Skin-scale-free Localization and Criticality under Möbius Boundary Conditions in a Non-Hermitian Ladder
• Fidelity zeros and Lee-Yang theory of quantum phase transitions
• Exceptional Non-Hermitian Topology Associated with Non-Toroidal Brillouin Zones
• An Explicit Wavefunction of the Interacting Non-Hermitian Spin-1/2 1D System
• Non-Hermitian topological superconductivity with symmetry-enriched spectral and eigenstate features
• Exceptional mode topological surface laser
• Non-Abelian geometry, topology, and dynamics of a nonreciprocal Su-Schrieffer-Heeger ladder
• Measuring topological invariants of even-dimensional line-gapped non-Hermitian systems through quench dynamics
• From Chiral Topological Dynamics to Chiral Topological Amplification: Real vs Imaginary Parameters in a Hermitian Bosonic Chain
• Exceptionally deficient topological square-root insulators
• Generalized Aubry-André-Harper model with power-law quasiperiodic potentials
• Multifractal statistics of non-Hermitian skin effect on the Cayley tree
• Topological spin textures in electronic non-Hermitian systems
• Unified Bulk-Entanglement Correspondence in Non-Hermitian Systems
• The quantum phase transitions of dimer chain driven by an imaginary ac field
• Non-Hermitian Hopf insulators
• Solution of Wave Acceleration and Non-Hermitian Jump in Nonreciprocal Lattices
• Symmetry and Topology of Monitored Quantum Dynamics
• Gaussian eigenstate pinning in non-Hermitian quantum mechanics
• Higher-order Topological Knots and the classification of non-Hermitian lattices under $C_n$ symmetry
• Magnetic Control of the Non-Hermitian Skin Effect in Two-Dimensional Lattices
• Non-Hermitian topological wall modes in rotating Rayleigh-Benard convection
• Adiabatic charge transport through non-Bloch bands
• Infinite-component $BF$ field theory: Connection of fracton order, Toeplitz braiding, and non-Hermitian amplification
• Topological Phases in Non-Hermitian Nonlinear-Eigenvalue Systems
• Breakdown of Non-Bloch Bulk-Boundary Correspondence and Emergent Topology in Floquet Non-Hermitian Systems
• Optimal spectral transport of non-Hermitian systems
• Entanglement manifestation of knot topology in a non-Hermitian lattice
• Anatomy of Higher-Order Non-Hermitian Skin and Boundary Modes
• Floquet Non-Bloch Formalism for a Non-Hermitian Ladder: From Theoretical Framework to Topolectrical Circuits
• Many-Body Neural Network Wavefunction for a Non-Hermitian Ising Chain
• Dynamical non-Hermitian systems: Fingerprints and pure dephasing induced protection effect
• Dynamical transition in non-Hermitian Chern insulator
• Intrinsic non-Hermitian topological phases
• Origin of Robust ${\mathbb{Z}}_2$ Topological Phases in Stacked Hermitian Systems: Non-Hermitian Level Repulsion
• Continuous phase transition induced by non-Hermiticity in the quantum contact process model
• Size-Dependent Skin Effect Transitions in Weakly Coupled Non-Reciprocal Chains
• Interplay of non-Hermitian skin effect and electronic correlations in the non-Hermitian Hubbard model via Real-space dynamical mean field theory
• Real spectra and phase transition of skin effect in nonreciprocal systems
• Tailoring Corner States and Exceptional Points in Altermagnets
• Topological photonics in nanoscaled systems with far field radiation and polarization singularities
• Topological Phase Transitions and Edge-State Transfer in Time-Multiplexed Quantum Walks
• Self-healing of non-Hermitian topological skin modes
• Winding-control mechanism of non-Hermitian systems
• Supermetal-insulator transition in a non-Hermitian network model
• 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
• Anatomy of Non-Hermitian Dynamical Quantum Phase Transitions
• Large Chern numbers in a dissipative dice model
• Scaling rule in critical non-Hermitian skin effect
• Illuminating the bulk-boundary correspondence of a non-Hermitian stub lattice with Majorana stars
• Majorana-like oscillation for edge states in one-dimensional topological chain with dissipative couplings
• Algebraic skin effect in two-dimensional non-Hermitian metamaterials
• Topology and edge modes surviving criticality in non-Hermitian Floquet systems
• Non-Hermitian Effects in the Su-Schrieffer-Heeger model: Exploring Substrate Coupling and Decoupling Dynamics
• Emergence of Hermitian topology from non-Hermitian knots
• Liouvillian topology and nonreciprocal dynamics in open Floquet chains
• Fate of Majorana zero modes by a modified real-space-Pfaffian method and mobility edges in a one-dimensional quasiperiodic lattice
• Arbitrary Control of Non-Hermitian Skin Modes via Disorder and An Electric Field
• Emulating non-Hermitian dynamics in a finite non-dissipative quantum system
• Recurrence method in Non-Hermitian Systems
• A new Berry phase term in parity-time symmetric non-Hermitian spin-1/2 quantum systems
• Non-Hermitian second-order topological insulator with point gap
• Liouvillian skin effects in two-dimensional electron systems at finite temperatures
• $q$th-root non-Hermitian Floquet topological insulators
• Robust interface-state laser in non-Hermitian micro-resonator arrays
• Geometric origin of self-intersection points in non-Hermitian energy spectra
• Beyond characteristic equations: A unified one-dimensional non-Bloch band theory via wavefunction data
• Nonreciprocal Local-Resonance Induced Complex Band Hybridization
• Observation of non-Hermitian point gap in photonic crystals
• Anomalous Point-Gap Interactions Unveil the Mirage Bath
• Engineering the non-Hermitian Su-Schrieffer-Heeger model with skin effects in Rydberg atom arrays
• Nonreciprocity Induced Fractional Nonlinear Thouless Pumping
• Supercharging exceptional points: Full-spectrum pairwise coalescence in non-Hermitian systems
• Interacting many-body non-Hermitian systems as Markov chains
• Zero Indirect Band Gap in Non-Hermitian Systems
• Revealing non-Hermitian band structures of photonic Floquet media
• 1D Spontaneous Symmetry Breaking in thermal equilibrium via Non-Hermitian Construction
• Algebraic States in Continuum in $d>1$ Dimensional Non-Hermitian Systems