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.

arXiv comment15 pages, 8 figures

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