Topological phases of non-Hermitian systems

Abstract

Recent experimental advances in controlling dissipation have brought about unprecedented flexibility in engineering non-Hermitian Hamiltonians in open classical and quantum systems. A particular interest centers on the topological properties of non-Hermitian systems, which exhibit unique phases with no Hermitian counterparts. However, no systematic understanding in analogy with the periodic table of topological insulators and superconductors has been achieved. In this paper, we develop a coherent framework of topological phases of non-Hermitian systems. After elucidating the physical meaning and the mathematical definition of non-Hermitian topological phases, we start with one-dimensional lattices, which exhibit topological phases with no Hermitian counterparts and are found to be characterized by an integer topological winding number even with no symmetry constraint, reminiscent of the quantum Hall insulator in Hermitian systems. A system with a nonzero winding number, which is experimentally measurable from the wave-packet dynamics, is shown to be robust against disorder, a phenomenon observed in the Hatano-Nelson model with asymmetric hopping amplitudes. We also unveil a novel bulk-edge correspondence that features an infinite number of (quasi-)edge modes. We then apply the K-theory to systematically classify all the non-Hermitian topological phases in the Altland-Zirnbauer classes in all dimensions. The obtained periodic table unifies time-reversal and particle-hole symmetries, leading to highly nontrivial predictions such as the absence of non-Hermitian topological phases in two dimensions. We provide concrete examples for all the nontrivial non-Hermitian AZ classes in zero and one dimensions. In particular, we identify a Z2 topological index for arbitrary quantum channels. Our work lays the cornerstone for a unified understanding of the role of topology in non-Hermitian systems.

arXiv comment31 pages, 18 figures, 2 tables, to appear in Physical Review X

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• Chiral polarizer based on encircling EP
• Classification of Matrix-Product Unitaries with Symmetries
• Entanglement Entropy of Non-Hermitian Free Fermions
• Topological synchronization of coupled nonlinear oscillators
• Topological and non-topological features of generalized Su-Schrieffer-Heeger models
• Topological Gapless Matters in Three-dimensional Ultracold Atomic Gases
• Observing dynamical currents in a non-Hermitian momentum lattice
• Non-Hermitian Maryland Model
• Non-Hermitian skin effects on many-body localized and thermal phases
• Localization, $\mathcal{P}\mathcal{T}$-Symmetry Breaking and Topological Transitions in non-Hermitian Quasicrystals
• Correlations at PT-symmetric quantum critical point
• Boundary Condition Independence of Non-Hermitian Hamiltonian Dynamics
• Lieb-Schultz-Mattis Theorem in Open Quantum Systems
• Interaction induced bi-skin effect in an exciton-polariton system
• Identifying Topological Phase Transitions in Experiments Using Manifold Learning
• Non-Hermitian Absorption Spectroscopy
• Continuous Dissipative Phase Transitions without Symmetry Breaking
• Chern insulators for electromagnetic waves in electrical circuit networks
• Symmetry Indicators for Inversion-Symmetric Non-Hermitian Topological Band Structures
• Quantum-Squeezing-Induced Point-Gap Topology and Skin Effect
• Hidden symmetries generate rigid folding mechanisms in periodic origami
• Classification of topological phases in one dimensional interacting non-Hermitian systems and emergent unitarity
• Symmetry indicator in non-Hermitian systems
• Cyclotron quantization and mirror-time transition on nonreciprocal lattices
• Topological phases protected by shifted sublattice symmetry in dissipative quantum systems
• R-DMFT study of a non-Hermitian skin effect for correlated systems: analysis based on a pseudo-spectrum
• Dynamic skin effects in non-Hermitian systems
• System size dependent topological zero modes in coupled topolectrical chains
• Universal platform of point-gap topological phases from topological materials
• Angle-Resolved Thermal Emission Spectroscopy Characterization of Non-Hermitian Meta-Crystals
• Observation of Quantum metric and non-Hermitian Berry curvature in a plasmonic lattice
• Unraveling the topology of dissipative quantum systems
• Bulk detection of time-dependent topological transitions in quenched chiral models
• Level statistics of extended states in random non-Hermitian Hamiltonians
• Quadratic pseudospectrum for identifying localized states
• Fourth-Order Exceptional Points in Correlated Quantum Many-Body Systems
• Topological properties of Floquet winding bands in a photonic lattice
• Compatibility of transport effects in non-Hermitian nonreciprocal systems
• Singular-Value Statistics of Non-Hermitian Random Matrices and Open Quantum Systems
• Always-Real-Eigenvalued Non-Hermitian Topological Systems
• General corner states in 2D SSH model with intracelluar next-nearest-neighbour hopping
• Impedance responses and size-dependent resonances in topolectrical circuits via the method of images
• The topological counterparts of non-Hermitian SSH models
• Quantum metric of non-Hermitian Su-Schrieffer-Heeger systems
• Controlling Exceptional Points with Light
• Exceptional points in the one-dimensional Hubbard model
• Emergent $\mathcal{P}\mathcal{T}$ symmetry in a double-quantum-dot circuit QED set-up
• Real spectra in non-Hermitian topological insulators
• Non-Hermitian pseudo mobility edge in a coupled chain system
• Skin modes in a nonlinear Hatano-Nelson model
• Continuum of Bound States in a Non-Hermitian Model
• Hybrid topological guiding mechanisms for photonic crystal fibers
• Amplification of quantum signals by the non-Hermitian skin effect
• Symmetry-protected exceptional and nodal points in non-Hermitian systems
• Floquet engineering and simulating exceptional rings with a quantum spin system
• Non-Hermitian skin effect edge
• Topology of multipartite non-Hermitian one-dimensional systems
• Manipulating non-Hermitian skin effect via electric fields
• Exponentially growing bulk Green functions as signature of nontrivial non-Hermitian winding number in one dimension
• Diagnosis of bulk phase diagram of non-reciprocal topological lattices by impurity modes
• Bound states and photon emission in non-Hermitian nanophotonics
• Level statistics of real eigenvalues in non-Hermitian systems
• Topological enhancement of non-normality in non-Hermitian skin effects
• Radiative topological biphoton states in modulated qubit arrays
• Generalized bulk-boundary correspondence in periodically driven non-Hermitian systems
• Adiabaticity in nonreciprocal Landau-Zener tunneling
• Interaction-induced Liouvillian skin effect in a fermionic chain with a two-body loss
• Stability of Time-Reversal Symmetry Protected Topological Phases
• Efficient algorithm to compute the second Chern number in four dimensional systems
• Protection of parity-time symmetry in topological many-body systems: non-Hermitian toric code and fracton models
• Anatomy of open-boundary bulk in multiband non-Hermitian systems
• Giant Emitters in a Structured Bath with Non-Hermitian Skin Effect
• Generalized Berry phase for a bosonic Bogoliubov system with exceptional points
• Erratic non-Hermitian skin localization
• Wannier-type photonic higher-order topological corner states induced solely by gain and loss
• Activity-induced phase transition in a quantum many-body system
• Bridging the gap between topological non-Hermitian physics and open quantum systems
• Dissipative analog of four-dimensional quantum Hall physics
• Stochastic non-Hermitian skin effect
• Double exceptional links in a three-dimensional dissipative cold atomic gas
• Dynamical robustness of topological end states in nonreciprocal Su-Schrieffer-Heeger models with open boundary conditions
• Anderson transition at complex energies in one-dimensional parity-time-symmetric disordered systems
• Out-of-time-ordered correlator in non-Hermitian quantum systems
• Entanglement dynamics in the many-body Hatano-Nelson model
• Reduction of one-dimensional non-Hermitian point-gap topology by correlations
• $\eta$-pairing ground states in the non-Hermitian Hubbard model
• Fermionic quantum cellular automata and generalized matrix product unitaries
• Mixed higher-order topology: boundary non-Hermitian skin effect induced by a Floquet bulk
• Symmetry-protected quantization of complex Berry phases in non-Hermitian many-body systems
• The Bulk-boundary Correspondence in Non-Hermitian Hopf-link Exceptional Line Semimetals
• Non-Hermiticity induces localization: good and bad resonances in power-law random banded matrices
• Disorder-induced exceptional and hybrid rings in Weyl/Dirac semimetals
• Polarization and entanglement spectrum in non-hermitian systems
• Geometry and superfluidity of the flat band in a non-Hermitian optical lattice
• Hyperbolic Nodal Band Structures and Knot Invariants
• Non-Hermitian phase-biased Josephson junctions
• Observation of scale-free localized states induced by non-Hermitian defects
• Generalized Quantum Geometric Tensor in a Non-Hermitian Exciton-Polariton System
• Edge theory of non-Hermitian skin modes in higher dimensions
• Light-driven Lifshitz transitions in non-Hermitian multi-Weyl semimetals
• Non-Hermitian topological end breathers
• Lyapunov equation in open quantum systems and non-Hermitian physics
• Nonlinear Topological Edge States in a non-Hermitian Array of Optical Waveguides Embedded in an Atomic Gas
• Engineering Dissipative Quasicrystals
• Point-gap topology with complete bulk-boundary correspondence in dissipative quantum systems
• Degeneracy and defectiveness in non-Hermitian systems with open boundary
• Effect of quantum jumps on non-Hermitian system
• Skin effect and dynamical delocalization in non-Hermitian quasicrystals with spin-orbit interaction
• Bulk-edge correspondence in nonunitary Floquet systems with chiral symmetry
• Topological phase transitions at finite temperature
• Non-reciprocal dynamics and the non-Hermitian skin effect of repulsively bound pairs
• The bosonic skin effect: boundary condensation in asymmetric transport
• Breaking and resurgence of symmetry in the non-Hermitian Su-Schrieffer-Heeger model in photonic waveguides
• Fate of exceptional points under interactions: Reduction of topological classifications
• Interaction effects on $\mathcal{P}\mathcal{T}$-symmetry breaking transition in atomic gases
• Robust localized zero-energy modes from locally embedded PT-symmetric defects
• Probing non-Hermitian phase transitions in curved space via quench dynamics
• Non-Hermitian Topology in Hermitian Topological Matter
• Anderson Delocalization in Strongly Coupled Disordered Non-Hermitian Chains
• Phase transitions and bunching of correlated particles in a non-Hermitian quasicrystal
• Topological zero modes and edge symmetries of metastable Markovian bosonic systems
• Non-Hermitian skin effect induced by Rashba-Dresselhaus spin-orbit coupling
• Observation of a topological edge state stabilized by dissipation
• Bulk Bogoliubov Fermi arcs in non-Hermitian superconducting systems
• Topological delocalization transitions and mobility edges in the nonreciprocal Maryland model
• Topological phase diagrams of exactly solvable non-Hermitian interacting Kitaev chains
• Dissipative Boundary State Preparation
• Irrational Non-Abelian Statistics for Non-Hermitian Generalization of Majorana Zero Modes
• Emergent Mott insulators and non-Hermitian conservation laws in an interacting bosonic chain with noninteger filling and nonreciprocal hopping
• Tutorial: Classifying Photonic Topology Using the Spectral Localizer and Numerical $K$-Theory
• Topological Protection in non-Hermitian Haldane Honeycomb Lattices
• Non-linear dynamics of the non-Hermitian Su-Schrieffer-Heeger model
• Machine learning non-Hermitian topological phases
• General criterion for non-Hermitian skin effects and Application: Fock space skin effects in many body systems
• Emergent non-Hermitian models
• Non-reciprocal Exciton-Polariton Ring Lattices
• Non-Hermitian CT-Symmetric Spectral Protection of Nonlinear Defect Modes
• Enhanced eigenvector sensitivity and algebraic classification of sublattice-symmetric exceptional points
• Hybrid scale-free skin effect in non-Hermitian systems: A transfer matrix approach
• Entanglement Dynamics in Anti-$\mathcal{P}\mathcal{T}$-Symmetric Systems
• Non-Hermitian Skin Effect in Periodically-Driven Dissipative Ultracold Atoms
• Damping transition in an open generalized Aubry-André-Harper model
• Nonreciprocal surface magnetoelastic dynamics
• Non-Hermitian Floquet phases with even-integer topological invariants in a periodically quenched two-leg ladder
• Non-normal Hamiltonian dynamics in quantum systems and its realization on quantum computers
• Emergent strength-dependent scale-free mobility edge in a non-reciprocal long-range Aubry-André-Harper model
• Asymmetric transfer matrix analysis of Lyapunov exponents in one-dimensional non-reciprocal quasicrystals
• Probing phase transitions in non-Hermitian systems with Multiple Quantum Coherences
• Hexagonally warped exceptional physics in multi-Weyl semimetals
• Anomalous Andreev Spectrum and Transport in Non-Hermitian Josephson Junctions
• Realizing exceptional points by Floquet dissipative couplings in thermal atoms
• Chiral state transfer under dephasing
• Bulk-boundary correspondence in extended trimer Su-Schrieffer-Heeger model
• Non-hermitian topology in multiterminal superconducting junctions
• Evidencing non-Bloch dynamics in temporal topolectrical circuits
• Ramsey interferometry of non-Hermitian quantum impurities
• Non-Abelian Braiding of Topological Edge Bands
• Modified Generalized-Brillouin-Zone Theory with On-site Disorders
• Non-Hermitian non-Abelian topological insulators with $PT$ symmetry
• Geometry-dependent skin effect and anisotropic Bloch oscillations in a non-Hermitian optical lattice
• Fractional Quantum Zeno Effect Emerging from Non-Hermitian Physics
• Topological triple phase transition in non-Hermitian quasicrystals with complex asymmetric hopping
• Universal subdiffusive behavior at band edges from transfer matrix exceptional points
• Non-Hermitian flatband generator in one dimension
• Topological characterization of non-Hermitian multiband systems using Majorana's Stellar Representation
• Making topologically trivial non-Hermitian systems nontrivial via gauge fields
• Observation of size-dependent boundary effects in non-Hermitian electric circuits
• Non-Hermitian multiterminal phase-biased Josephson junctions
• Dynamical preparation of a steady ODLRO state in the Hubbard model with local non-Hermitian impurity
• Real spectra, Anderson localization, and topological phases in one-dimensional quasireciprocal systems
• Topological transport in the steady state of a quantum particle with dissipation
• Competition of non-Hermitian skin effect and topological localization of corner states observed in circuits
• Correlation effects on non-Hermitian point-gap topology in zero dimension: reduction of topological classification
• Complex Berry phase and imperfect non-Hermitian phase transitions
• Non-Hermitian spectral flows and Berry-Chern monopoles
• Exact formulas of the end-to-end Green's functions in non-Hermitian systems
• Exceptional degeneracies in non-Hermitian Rashba semiconductors
• Topological Signatures in Quantum Transport in Anomalous Floquet-Anderson Insulators
• Quantum criticality in interacting bosonic Kitaev-Hubbard models
• Non-Hermitian topological mobility edges and transport in photonic quantum walks
• Critical non-Hermitian topology induced quantum sensing
• Exceptional points as signatures of dynamical magnetic phase transitions
• Emergent conservation in Floquet dynamics of integrable non-Hermitian models
• Symmetry-protected localized states at defects in non-Hermitian systems
• Algebraic non-Hermitian skin effect and generalized Fermi surface formula in arbitrary dimensions
• Anderson localization versus hopping asymmetry in a disordered lattice
• Chiral metals and entrapped insulators in a one-dimensional topological non-Hermitian system
• Non-Hermitian edge burst without skin localizations
• Filling up complex spectral regions through non-Hermitian disordered chains
• Engineering non-Hermitian Second Order Topological Insulator in Quasicrystals
• Field theory of non-Hermitian disordered systems
• Extension of Noether's theorem in PT-symmetric systems and its experimental demonstration in an optical setup
• Quantum Metric Unveils Defect Freezing in Non-Hermitian Systems
• Many-body Non-Hermitian Skin Effect At Finite Temperatures
• Unsupervised learning of topological phase diagram using topological data analysis
• Non-Hermitian second-order topological superconductors
• Identifying non-Hermitian critical points with quantum metric
• Scaling laws for non-Hermitian skin effect with long-range couplings
• The simulation of non-Hermitian disordered system in linear circuits
• Topological superconductivity enhanced by exceptional points
• A renormalization group approach to non-Hermitian topological quantum criticality
• Exceptional point induced lasing dynamics in a non-Hermitian system
• Non-Hermitian topological ohmmeter
• Quantum Dynamics with Stochastic Non-Hermitian Hamiltonians
• Topological atomic spinwave lattices by dissipative couplings
• Real Non-Hermitian Energy Spectra Without Any Symmetry
• $\mathcal{P}\mathcal{T}$ symmetry of the Su-Schrieffer-Heeger model with imaginary boundary potentials and next-nearest-neighboring coupling
• Quantum Electrodynamics of Non-Hermitian Dirac Fermions
• Topological Classification of Excitations in Quadratic Bosonic Systems
• Engineering Interaction Dynamics in Active Resonant Photonic Structures
• Universal characteristics of one-dimensional non-Hermitian superconductors
• Finite-size Topology
• Quantum state discrimination in a PT-symmetric system
• Exceptional dynamics of interacting spin liquids
• Non-Hermitian Fabry-Perot Resonances in a PT-symmetric system
• Driven-dissipative topological phases in parametric resonator arrays
• Braiding Topology of Non-Hermitian Open-Boundary Bands
• Exact complex mobility edges and flagellate spectra for non-Hermitian quasicrystals with exponential hoppings
• From Ergodicity to Many-Body Localization in a One-Dimensional Interacting Non-Hermitian Stark System
• Exponentially Enhanced non-Hermitian Cooling
• Infernal and Exceptional Edge Modes: Non-Hermitian Topology Beyond the Skin Effect
• Robust quantum boomerang effect in non-Hermitian systems
• Observation of disorder-induced boundary localization
• Non-Hermitian topological phases and skin effects in kagome lattices
• Dynamical signatures of point-gap Weyl semimetal
• Liouvillian skin effects and fragmented condensates in an integrable dissipative Bose-Hubbard model
• Symmetric non-Hermitian skin effect with emergent nonlocal correspondence
• Evolution of spectral topology in one-dimensional long-range nonreciprocal lattices
• Metal-insulator transition in a 2D system of chiral unitary class
• Pseudospin-orbit coupling and non-Hermitian effects in the Quantum Geometric Tensor of a plasmonic lattice
• Dissipative Quantum Chaos unveiled by Stochastic Quantum Trajectories
• Nonreciprocal Amplification Transition in a Driven-Dissipative Quantum Network
• Efficient variational approach to dynamics of a spatially extended bosonic Kondo model
• Alice string in Non-Hermitian Systems
• Point-Gap Bound States in Non-Hermitian Systems
• Two-dimensional non-Hermitian topological phases induced by asymmetric hopping in a one-dimensional superlattice
• Creating and controlling exceptional points of non-Hermitian Hamiltonians via homodyne Lindbladian invariance
• Pseudomagnetic suppression of non-Hermitian skin effect
• Correlations and Krylov spread for a non-Hermitian Hamiltonian: Ising chain with a complex-valued transverse magnetic field
• Theory of non-Hermitian fermionic superfluidity on a honeycomb lattice: Interplay between exceptional manifolds and van Hove Singularity
• Ubiquity of the quantum boomerang effect in Hermitian Anderson-localized systems
• Inducing a many-body topological state of matter through Coulomb-engineered local interactions
• Topological transitions in quantum jump dynamics: Hidden exceptional points
• Many-body entanglement and spectral clusters in the extended hard-core bosonic Hatano-Nelson model
• Non-Hermitian Origin of Detachable Boundary States in Topological Insulators
• Many-body phase transitions in a non-Hermitian Ising chain
• Topology of rotating stratified fluids with and without background shear flow
• A simple approach to characterizing band topology in bosonic pairing Hamiltonians
• Construction of Non-Hermitian Parent Hamiltonian from Matrix Product States
• Unravelling the edge spectra of non-Hermitian Chern insulators
• Topological modes in stellar oscillations
• Bulk-edge correspondence and trapping at a non-Hermitian topological interface
• Hermitian Topologies originating from non-Hermitian braidings
• Non-Hermitian minimal Kitaev chains
• Giant non-reciprocity and gyration through modulation-induced Hatano-Nelson coupling in integrated photonics
• Observables in non-Hermitian systems: A methodological comparison
• Exceptional Non-Hermitian Phases in Disordered Quantum Wires
• Anomalous dynamical response of non-Hermitian topological phases
• Nonhermitian defect states from lifetime differences
• Nontrivial worldline winding in non-Hermitian quantum systems
• Physics of PT-Symmetric Quantum Systems at Finite Temperature
• Calculations of Chern number: equivalence of real-space and twisted-boundary-condition formulae
• Complexity of Fermionic Dissipative Interactions and Applications to Quantum Computing
• Generalized Fermion Doubling Theorems: Classification of 2D Nodal Systems in Terms of Wallpaper Groups
• State-dependent Topological Invariants and Anomalous Bulk-Boundary Correspondence in non-Hermitian Topological Systems
• Dissipation Induced Flat Bands
• Multifractality of many-body non-Hermitian skin effect
• Interferometric geometry from symmetry-broken Uhlmann gauge group with applications to topological phase transitions
• Non-reciprocal breathing solitons
• Imaginary gap-closed points and dynamics in a class of dissipative systems
• Coexistence of stable and unstable population dynamics in a nonlinear non-Hermitian mechanical dimer
• Topological quantum optical states in quasiperiodic cold atomic chains
• Adaptive variational low-rank dynamics for open quantum systems
• The Interplay of Finite and Infinite Size Stability in Quadratic Bosonic Lindbladians
• Hopf Bifurcation of Nonlinear Non-Hermitian Skin Effect
• Majorana zero modes, unconventional real-complex transition and mobility edges in a one-dimensional non-Hermitian quasi-periodic lattice
• Quantum metric dependent anomalous velocity in systems subject to complex electric fields
• Non-Hermitian topological phase transitions in superlattices and the optical Dirac equation
• Nonlinear perturbation of a high-order exceptional point: skin discrete breathers and the hierarchical power-law scaling
• Selective and tunable excitation of topological non-Hermitian skin modes
• Work statistics in non-Hermitian evolutions with Hermitian endpoints
• Mesoscopic transport signatures of disorder-induced non-Hermitian phases
• Correlation-induced phase transitions and mobility edges in an interacting non-Hermitian quasicrystal
• Floquet Exceptional Topological Insulator
• Exceptional points and non-Hermitian skin effects under nonlinearity of eigenvalues
• Hidden Critical Points in the Two-Dimensional $O(n>2)$ model: Exact Numerical Study of a Complex Conformal Field Theory
• Entanglement transitions in a periodically driven non-Hermitian Ising chain
• Electrically tunable liquid-crystal metasurfaces with patterned birefringence and dichroism
• Role of Topology in Relaxation of One-Dimensional Stochastic Processes
• Investigation of a non-Hermitian edge burst with time-dependent perturbation theory
• Symmetry-Protected Topological Phase for Spin-Tensor-Momentum-Coupled Ultracold Atoms
• Topological skyrmion phases of matter
• Fundamental constraints on the observability of non-Hermitian effects in passive systems
• Non-Hermitian boost deformation
• From scale-free to Anderson localization: a size-dependent transition
• Dynamically Induced Exceptional Phases in Quenched Interacting Semimetals
• Role of Bath-Induced Many-Body Interactions in the Dissipative Phases of the Su-Schrieffer-Heeger Model
• Lindbladian dynamics with loss of quantum jumps
• Hermitian chiral boundary states in non-Hermitian topological insulators
• Generalized multifractality in 2D disordered systems of chiral symmetry classes
• Topological band theory of a generalized eigenvalue problem with Hermitian matrices: Symmetry-protected exceptional rings with emergent symmetry
• Exact non-Hermitian mobility edges and robust flat bands in two-dimensional Lieb lattices with imaginary quasiperiodic potentials
• Topological transitions in dissipatively coupled Su-Schrieffer-Heeger models
• Complex semiclassical theory for non-Hermitian quantum systems
• A symmetry-protected exceptional ring in a photonic crystal with negative index media
• Engineering imaginary stark ladder in a dissipative lattice: passive $\mathcal{P}\mathcal{T}$ symmetry, K symmetry and localized damping
• Non-Hermitian skin effect enforced by nonsymmorphic symmetries
• Topological $n$-root Su-Schrieffer-Heeger model in a non-Hermitian photonic ring system
• Generalized Lieb's theorem for noninteracting non-Hermitian $n$-partite tight-binding lattices
• Non-Hermitian control of localization in mosaic photonic lattices
• Discriminant indicators with generalized inversion symmetry
• Equivalence and superposition of real and imaginary quasiperiodicities
• Emergent non-Hermitian localization phenomena in the synthetic space of zero-dimensional bosonic systems
• Extended imaginary gauge transformation in a general nonreciprocal lattice
• Relationship between the Electronic Polarization and the Winding Number in Non-Hermitian Systems
• Surface exceptional points in a topological Kondo insulator
• Fate of non-Hermitian free fermions with Wannier-Stark ladder
• Information constraint in open quantum systems
• Non-Hermitian three-dimensional two-band Hopf insulator
• Correlations in non-Hermitian systems and Diagram techniques for the steady state
• Anomalous second-order skin modes in Floquet non-Hermitian systems
• Disorder-Protected Quantum State Transmission through Helical Coupled-Resonator Waveguides
• Bulk-Edge Correspondence for Point-Gap Topological Phases in Junction Systems
• Mode-Shell correspondence, a unifying phase space theory in topological physics -- Part I: Chiral number of zero-modes
• Non-Hermitian Quantum Fractals
• Non-Floquet engineering in periodically driven non-Hermitian systems
• Skin Effect Induced Anomalous Dynamics from Charge-Fluctuating Initial States
• Eigenstate clustering around exceptional points
• Quantum quenches in a pseudo-Hermitian Chern insulator
• Boundary-dependent dynamical instability of bosonic Green's function: Dissipative Bogoliubov-de Gennes Hamiltonian and its application to non-Hermitian skin effect
• Design nearly optimal quantum algorithm for linear differential equations via Lindbladians
• Emergent multi-loop nested point gap in a non-Hermitian quasiperiodic lattice
• Diagnosing Quantum Phases Using Long-Range Two-Site Quantum Resource Behaviors
• Anomalous pumping in the non-Hermitian Rice-Mele model
• Edge states in a non-Hermitian topological crystalline insulator
• General mapping of one-dimensional non-Hermitian mosaic models to non-mosaic counterparts: Mobility edges and Lyapunov exponents
• Effective impurity behavior emergent from non-Hermitian proximity effect
• Universal spectral moment theorem and its applications in non-Hermitian systems
• Interaction-Induced Second-Order Skin Effect
• Dynamical signatures of the Yang-Lee edge singularity in non-Hermitian systems
• Hilbert space fragmentation imposed real spectrum of non-Hermitian systems
• Field Theoretical Study of Disorder in Non-Hermitian Topological Models
• Defect bulk-boundary correspondence of topological skyrmion phases of matter
• Unveiling Eigenstate Thermalization for Non-Hermitian systems
• $\mathcal{P}\mathcal{T}$ symmetry of a square-wave modulated two-level system
• Localization and topological transitions in generalized non-Hermitian SSH models
• Accelerating multipartite entanglement generation in non-Hermitian superconducting qubits
• Ultrathin acoustic parity-time symmetric metasurface cloak
• Topological invariants of complex energy plane in non-Hermitian systems
• Fate of pseudo mobility-edge and multiple states in non-Hermitian Wannier-Stark lattice
• Localization and mobility edges in non-Hermitian continuous quasiperiodic systems
• Nonequilibrium steady states of Bose-Einstein condensates with a local particle loss in double potential barriers
• Lindbladian versus Postselected Non-Hermitian Topology
• Visualizing Topology of Real-Energy Gapless Phase Arising from Exceptional Point
• Extrinsic topology of Floquet anomalous boundary states in quantum walks
• Chiral-Extended Photon-Emitter Dressed States in Non-Hermitian Topological Baths
• Exceptional magic angles in non-Hermitian twisted bilayer graphene
• Non-Bloch dynamics and topology in a classical non-equilibrium process
• Coexistence of non-Hermitian skin effect and extended states in one-dimensional nonreciprocal lattices
• Edge-dependent anomalous topology in synthetic photonic lattices subject to discrete step walks
• Quantization of the mean decay time for non-Hermitian quantum systems
• General theory for infernal points in non-Hermitian systems
• Quantum geometry of bosonic Bogoliubov quasiparticles
• Selection Rule for Topological Amplifiers in Bogoliubov de Gennes Systems
• Floquet engineering flat bands for bosonic fractional quantum Hall in small lattices
• Non-Hermitian skin effect and lasing of absorbing open-boundary modes in photonic crystals
• Unconventional and robust light-matter interactions based on the non-Hermitian skin effect
• Topological study of a Bogoliubov-de Gennes system of pseudo spin-$1/2$ bosons with conserved magnetization in a honeycomb lattice
• Krein-unitary Schrieffer-Wolff transformation and band touchings in bosonic Bogoliubov-de Gennes and other Krein-Hermitian Hamiltonians
• Complete absorption of topologically protected waves
• Quantum circuit for measuring an operator's generalized expectation values and its applications to non-Hermitian winding numbers
• Implementing non-Abelian Hatano-Nelson model in electric circuits
• Universal hard-edge statistics of non-Hermitian random matrices
• Phase Transitions and Virtual Exceptional Points in Quantum Emitters Coupled to Dissipative Baths
• Real spectra in one-dimensional single-band non-Hermitian Hamiltonians
• Non-Hermitian superconducting diode effect
• Topological Insulators with Hybrid-order Boundary States
• Competing topological phases in a non-Hermitian time-reversal symmetry-broken Bernevig-Hughes-Zhang model
• Topological enhancement of exciton-polariton coherence with non-Hermitian morphing
• Wannier-Stark localization in one-dimensional amplitude-chirped lattices
• Protection of Correlation-Induced Phase Instabilities by Exceptional Susceptibilities
• Topological modes and spectral flows in inhomogeneous PT-symmetric continuous media
• Non-Hermitian quantum gases: a platform for imaginary time crystals
• The Quantum Skin Hall Effect
• Topological Invariant for Multi-Band Non-hermitian Systems with Chiral Symmetry
• Observation of non-Hermitian many-body skin effects in Hilbert space
• Dissipation Enhanced Unidirectional Transport in Topological Systems
• Parsing skin effect in a non-Hermitian spinless BHZ-like model
• Efimov physics in the complex plane
• Abnormal Frequency Response Determined by Saddle Points in Non-Hermitian Crystal Systems
• Supersymmetric Free Fermions and Bosons: Locality, Symmetry and Topology
• Phase diagram of non-Hermitian BCS superfluids in a dissipative asymmetric Hubbard model
• Quantum quench dynamics in the Luttinger liquid phase of the Hatano-Nelson model
• Anomalous hybridization of spectral winding topology in quantized steady-state responses
• Yukawa-Lorentz symmetry of interacting non-Hermitian birefringent Dirac fermions
• Generalized topological bulk-edge correspondence in bulk-Hermitian continuous systems with non-Hermitian boundary conditions
• Electronic polarization in non-Bloch band theory
• Dissipative two-dimensional Raman lattice
• Non-reciprocity is necessary for robust dimensional reduction and strong responses in stochastic topological systems
• Localization transition in non-Hermitian systems depending on reciprocity and hopping asymmetry
• Unsupervised interpretable learning of topological indices invariant under permutations of atomic bands
• Inner non-Hermitian skin effect on Bethe lattice
• Berry curvature inside parity-time-symmetry protected exceptional surface
• Topological phase transition in fluctuating imaginary gauge fields
• Gain-loss-induced non-Abelian Bloch braids
• Quantum Sensing with Driven-Dissipative Su-Schrieffer-Heeger Lattices
• Characterizing phase transitions and criticality in non-Hermitian extensions of the XY model
• Exceptional Heavy-Fermion Semimetals in Three Dimensions
• Measuring Non-Hermitian Topological Invariants Directly from Quench Dynamics
• Inverse Design of Winding Tuple for Non-Hermitian Topological Edge Modes
• Topology of Discrete Quantum Feedback Control
• One-dimensional non-Hermitian band structures as Riemann surfaces
• Non-Hermitian $C_{NH}=2$ Chern insulator protected by generalized rotational symmetry
• Liouvillian skin effect in quantum neural networks
• Spectrum collapse of disordered Dirac Landau levels as topological non-Hermitian physics
• Anomalous spectrum in a non-Hermitian quasiperiodic chain
• Spontaneous Formation of Exceptional Points at the Onset of Magnetism
• Emergent non-Hermitian physics in generalized Lotka-Volterra model
• Symmetries, Conservation Laws and Entanglement in Non-Hermitian Fermionic Lattices
• Transfer learning from Hermitian to non-Hermitian quantum many-body physics
• Topological directed amplification
• Lack of near-sightedness principle in non-Hermitian systems
• Machine learning of mirror skin effects in the presence of disorder
• Work statistics and generalized Loschmidt echo for the Hatano-Nelson model
• Non-Quantized Edge Channel Conductance and Zero Conductance Fluctuation in Non-Hermitian Chern Insulators
• Boundary-driven many-body phase transitions in a non-Hermitian disordered fermionic chain
• Two-dimensional lattice with an imaginary magnetic field
• Wave-packet and entanglement dynamics in a non-Hermitian many-body system
• The product of two independent Su-Schrieffer-Heeger chains yields a two-dimensional Chern insulator
• Topological Operations Around Exceptional Points via Shortcuts to Adiabaticity
• Non-Hermitian theory of valley excitons in two-dimensional semiconductors
• Antichiral and trap-skin dynamics in a nonreciprocal bosonic two-leg ladder with artificial magnetic flux
• Enhancement of vibrationally assisted energy transfer by proximity to exceptional points, probed by fluorescence-detected vibrational spectroscopy
• Exceptional second-order topological insulators
• Adiabatic Transformations in Dissipative and Non-Hermitian Phase Transitions
• Sensitivity of topological edge states in a non-Hermitian dimer chain
• Spin-Depairing-Induced Exceptional Fermionic Superfluidity
• Distinguishability Transitions in Non-Unitary Boson Sampling Dynamics
• Quantized electrical, thermal, and spin transports of non-Hermitian clean and dirty two-dimensional topological insulators and superconductors
• Breakdown of Linear Spin-Wave Theory in a Non-Hermitian Quantum Spin Chain
• Phase transitions in non-Hermitian superlattices
• $K$-theory classification of Wannier localizability and detachable topological boundary states
• Non-Hermitian dynamical topological winding in photonic mesh lattices
• Non-Hermitian topological quantum states in a reservoir-engineered transmon chain
• Topology and its detection in a dissipative Aharonov-Bohm chain
• Delocalization of interacting directed polymers on a periodic substrate: Localization length and critical exponents from non-Hermitian spectra
• Fate of localization features in a one-dimensional non-Hermitian flat-band lattice with quasiperiodic modulations
• Manipulating Spectral Windings and Skin Modes through Nonconservative Couplings
• Emergent Topology in Many-Body Dissipative Quantum Matter
• Recognizing critical lines via entanglement in non-Hermitian systems
• Fate of symmetry protected coherence in open quantum system
• Discriminant indicator with generalized rotational symmetry
• Winding Topology of Multifold Exceptional Points
• Dual Symmetry Classification of Non-Hermitian Systems and ${\mathbb{Z}}_2$ Point-Gap Topology of a Non-Unitary Quantum Walk
• Entanglement Spectrum Dynamics as a Probe for Non-Hermitian Bulk-Boundary Correspondence in Systems with Periodic Boundaries
• Non-Hermitian synthetic lattices with light-matter coupling
• Composite Quantum Phases in Non-Hermitian Systems
• Mobility rings in a non-Hermitian non-Abelian quasiperiodic lattice
• Topological characteristics of gap closing points in nonlinear Weyl semimetals
• Non-Hermitian ${\mathbb{Z}}_4$ skin effect protected by glide symmetry
• Model non-Hermitian topological operators without skin effect: A general principle of construction
• Theory for the spectral splitting exponent of exceptional points
• The global phase diagram of the cluster-XY spin chain with dissipation
• Controllable suppression of Non-Hermitian skin effects
• Transport and integrability-breaking in non-Hermitian many-body quantum systems
• Coalescing hardcore-boson condensate states with nonzero momentum
• Pseudo-Hermitian Topology of Multiband Non-Hermitian Systems
• Magnetization in a non-equilibrium quantum spin system
• Hinge non-Hermitian skin effect in the single-particle properties of a strongly correlated f-electron system
• Direct Measurement of a Non-Hermitian Topological Invariant in a Hybrid Light-Matter System
• Topological phases of many-body non-Hermitian systems
• Topology of ultra-localized insulators and superconductors
• Hermitian and non-Hermitian topology in active matter
• Slow approach to adiabaticity in many-body non-Hermitian systems: the Hatano-Nelson Model
• Exceptional topology in non-Hermitian twisted bilayer graphene
• Random non-Hermitian action theory for stochastic quantum dynamics: from canonical to path integral quantization
• Band structures under non-Hermitian periodic potentials: Connecting nearly-free and bi-orthogonal tight-binding models
• Two-body interaction induced phase transitions and intermediate phases in nonreciprocal non-Hermitian quasicrystals
• Non-Hermitian catalysis of spontaneous symmetry breaking on Euclidean and hyperbolic lattices
• Topological analysis of the complex SSH model using the quantum geometric tensor
• Non-Hermitian Multipole Skin Effects Challenge Localization
• Exact multiple complex mobility edges and quantum state engineering in coupled 1D quasicystals
• Gauge Field Induced Unconventional Skin Effect in Spinful Non-Hermitian Systems
• Dissipative phase transition of interacting non-reciprocal fermions
• Fractional Thouless pumping of solitons: a unique manifestation of bulk-edge correspondence of nonlinear eigenvalue problems
• Anderson-skin dualism: A boundary-dependent effect in non-Hermitian disordered coupled systems
• Topological invariants and topological charges in photonic systems
• Semi-localization transition driven by a single asymmetrical tunneling
• Defect-driven incoherent skin localization
• Quantum geometrical effects in non-Hermitian systems
• Recent advances in the combination of nonlinearity and exceptional points
• Reconfigurable Non-Hermitian Soliton Combs using Dissipative Couplings and Topological Windings
• Alternating quantum-emitter chains: Exceptional-point phase transition, edge state, and quantum walks
• Dissolution of the non-Hermitian skin effect in one-dimensional lattices with linearly varying nonreciprocal hopping
• Mixedness timescale in non-Hermitian quantum systems
• Topological extension including quantum jump
• Phase Diagram of a Non-Hermitian Chern Insulator: Destabilization of Chiral Edge States and Bulk-Boundary Correspondence
• Controlling the direction of topological transport in a non-Hermitian time-reversal symmetric Floquet ladder
• Exceptional Points, Bulk-Boundary Correspondence, and Entanglement Properties for a Dimerized Hatano-Nelson Model with Staggered Potentials
• Unified Bulk-Entanglement Correspondence in Non-Hermitian Systems
• Nonequilibrium protection effect and spatial localization of noise-induced fluctuations: Quasi-one-dimensional driven lattice gas with partially penetrable obstacle
• PT-symmetric Non-Hermitian Hopf Metal
• Quantum transient heat transport in the hyper-parametric oscillator
• Generalized Aubry-André-Harper model with power-law quasiperiodic potentials
• Universal distributions from non-Hermitian Perturbation of Zero-Modes
• Random non-Hermitian Hamiltonian framework for symmetry breaking dynamics
• From Chiral Topological Dynamics to Chiral Topological Amplification: Real vs Imaginary Parameters in a Hermitian Bosonic Chain
• Non-Hermitian Hopf insulators
• Dissipation-driven topological phase transitions in open quantum systems independent of system Hamiltonian
• An effective curved space-time geometric theory of generic twist angle graphene with application to a rotating bilayer configuration
• Exceptional mode topological surface laser
• Measuring topological invariants of even-dimensional line-gapped non-Hermitian systems through quench dynamics
• Critical phase boundary and finite-size fluctuations in Su-Schrieffer-Heeger model with random inter-cell couplings
• Multitype entanglement dynamics induced by exceptional points
• Exceptional Non-Hermitian Topology Associated with Non-Toroidal Brillouin Zones
• Dynamic transition of the density-matrix topology under parity-time symmetry
• Unifying Anderson transitions and topological amplification in non-Hermitian chains
• Interactions-disorder duality and critical phenomena in nodal semimetals, dilute gases and other systems
• From Hermitian critical to non-Hermitian point-gapped phases
• Non-Hermitian topological superconductivity with symmetry-enriched spectral and eigenstate features
• Topological Defect Propagation to Classify Knitted Fabrics
• Nonequilibrium electron distribution function in a voltage-biased nanowire: A nonequilibrium Green's function approach
• Band topology of pseudo-Hermitian phases through tensor Berry connections and quantum metric
• Topological spin textures in electronic non-Hermitian systems
• Non-Abelian geometry, topology, and dynamics of a nonreciprocal Su-Schrieffer-Heeger ladder
• Multifractal statistics of non-Hermitian skin effect on the Cayley tree
• Coherent transfer of topological domain walls
• Symmetry and Topology of Monitored Quantum Dynamics
• Entanglement manifestation of knot topology in a non-Hermitian lattice
• Disorder-driven exceptional points and concurrent topological phase transitions in non-Hermitian systems
• Scattering States in One-Dimensional Non-Hermitian Baths
• Non-Hermitian magnetic moment
• Breakdown of Non-Bloch Bulk-Boundary Correspondence and Emergent Topology in Floquet Non-Hermitian Systems
• Dynamical non-Hermitian systems: Fingerprints and pure dephasing induced protection effect
• Topological Amplification of the Bosonic Kitaev Chain with Non-Uniform Loss
• Topological photonics in nanoscaled systems with far field radiation and polarization singularities
• Unified Multipole Bott Indices for Non-Hermitian Skin Effect in Different Orders
• Constructing qubit edge states by inverse-designing the electromagnetic environment
• Symmetry classification correspondence between quadratic Lindbladians and their steady states
• Exploring Metamaterial Lasers through Non-Hermitian Scattering Formalism
• Adiabatic charge transport through non-Bloch bands
• Noisy Stark probes as quantum-enhanced sensors
• Optimal spectral transport of non-Hermitian systems
• Floquet Non-Bloch Formalism for a Non-Hermitian Ladder: From Theoretical Framework to Topolectrical Circuits
• Nonequilibrium Nonlinear Effects and Dynamical Boson Condensation in a Driven-Dissipative Wannier-Stark Lattice
• Non-hermitian off-diagonal magnetic response of Dirac fermions
• Scaling of pseudospectra in exponentially sensitive lattices
• Real spectra and phase transition of skin effect in nonreciprocal systems
• Third-quantized master equations as a classical Ornstein-Uhlenbeck process
• Magnetic Control of the Non-Hermitian Skin Effect in Two-Dimensional Lattices
• Zero modes and index theorems for non-Hermitian Dirac fermions
• Origin of Robust ${\mathbb{Z}}_2$ Topological Phases in Stacked Hermitian Systems: Non-Hermitian Level Repulsion
• Quantum-vacuum-protected topological edge polaritons
• Observation of novel robust edge states without bulk-boundary correspondence in non-Hermitian quantum walks
• Recent progress on disorder-induced topological phases
• Non-Hermitian wave-packet dynamics and its realization within a non-Hermitian chiral cavity
• Interplay of non-Hermitian skin effect and electronic correlations in the non-Hermitian Hubbard model via Real-space dynamical mean field theory
• Coexistence of extended and localized states in one-dimensional non-Hermitian Anderson model
• Intrinsic non-Hermitian topological phases
• Multi-block exceptional points in open quantum systems
• Critical properties in the non-Hermitian Aubry-Andre-Stark model
• Anatomy of Higher-Order Non-Hermitian Skin and Boundary Modes
• Hybrid Higher-Order Skin Topological Modes in the Two-Dimensional Su-Schrieffer-Heeger Model with Nonreciprocal Hoppings
• Size-Dependent Skin Effect Transitions in Weakly Coupled Non-Reciprocal Chains
• Gaussian eigenstate pinning in non-Hermitian quantum mechanics
• Dynamical transition in non-Hermitian Chern insulator
• Anatomy of Non-Hermitian Dynamical Quantum Phase Transitions
• Large Chern numbers in a dissipative dice model
• Hall conductance of a non-Hermitian two-band system with k-dependent decay rates
• Topology of the simplest gene switch
• Exceptional flat bands in bipartite non-Hermitian lattices
• Complex-valued in-medium potential between heavy impurities in ultracold atoms
• Emergence of non-trivial phases in interacting non-Hermitian quasiperiodic chains with power-law hopping
• Zero Indirect Band Gap in Non-Hermitian Systems
• Anomalous Point-Gap Interactions Unveil the Mirage Bath
• Physical relevance of time-independent scattering calculations in non-Hermitian systems: The role of time-growing bound states
• Symmetry and Topology of Successive Quantum Feedback Control
• Continuum Landau surface states in a non-Hermitian Weyl semimetal
• 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
• Liouvillian topology and nonreciprocal dynamics in open Floquet chains
• Arbitrary Control of Non-Hermitian Skin Modes via Disorder and An Electric Field
• Coupled-wire construction of non-Abelian higher-order topological phases
• Geometric phase from encircling an exceptional point of a quantum resonance in the complex-scaling method
• Covariant formulation of the Berry connection in non-Hermitian systems
• Quasiperiodic Skin Criticality in an Exactly Solvable Non-Hermitian Quasicrystal
• Topology and edge modes surviving criticality in non-Hermitian Floquet systems
• Nonreciprocity Induced Fractional Nonlinear Thouless Pumping
• Floquet topological properties in the Non-Hermitian long-range system with complex hopping amplitudes
• Coexistence of topological Anderson insulator and multifractal critical phase in a non-Hermitian quasicrystal
• Engineering qubit dynamics in open systems with photonic synthetic lattices
• Limitations of SVD-Based Diagnostics for Non-Hermitian Many-Body Localization with Time-Reversal Symmetry
• Spectroscopic Signatures of a Liouvillian Exceptional Spectral Phase in a Collective Spin
• Anomalous Non-Hermitian Topological Anderson Insulator
• Phase-Space Topology and Spectral Flow in Screened Magnetized Plasmas
• Bulk-boundary correspondence in topological two-dimensional non-Hermitian systems: Toeplitz operators and singular values
• Lattice-induced wavefunction effects on trapped superfluids
• Recurrence method in Non-Hermitian Systems
• Simulating monitoring-induced topological phase transitions with small systems
• Dynamic manifestation of exception points in a non-Hermitian continuous model with an imaginary periodic potential
• Presence of temporal dynamical instabilities in topological insulator lasers
• Phase transition from Weyl to self-linked semimetal using bi-circular laser
• Proof of bulk-edge correspondence for band topology by Toeplitz algebra
• Generic non-Hermitian mobility edges in a class of duality-breaking quasicrystals
• 1D Spontaneous Symmetry Breaking in thermal equilibrium via Non-Hermitian Construction
• A way to hypo-elastic artificial materials without a strain potential and displaying flutter instability
• Synthetic high-order PT symmetry in a single coil resonator
• Exceptional Luttinger Liquids from sublattice dependent interaction
• Anti-Holomorphic Modes in Vortex Lattices
• Correspondence between non-Hermitian topology and directional amplification in the presence of disorder
• Quantifying non-Hermiticity using single- and many-particle quantum properties
• Interferometric Geometric Phases of $\mathcal{P}\mathcal{T}$-symmetric Quantum Mechanics
• Decimation technique for open quantum systems: a case study with driven-dissipative bosonic chains
• Self-healing of non-Hermitian topological skin modes
• Anomalous Transport Induced by Non-Hermitian Anomalous Berry Connection in Non-Hermitian Systems
• Mechanical activity and odd elasticity of passive, 2D chiral metamaterials
• Non-Hermitian Higher-Order Dirac Semimetals
• Non-Hermitian Higher-Order Weyl Semimetals
• Magnetic field effects on the Kitaev model coupled to environment
• Immutable quantized transport in Floquet chains
• Dissipation-induced bound states as a two-level system
• Emergence of Hermitian topology from non-Hermitian knots
• Non-orientable Exceptional Points in Twisted Boundary Systems
• Emergence of Imaginary Time Crystals in the non-Hermitian Su-Schrieffer-Heeger model
• Loss-driven topological transitions in lasing
• Liouvillian skin effects in two-dimensional electron systems at finite temperatures
• Illuminating the bulk-boundary correspondence of a non-Hermitian stub lattice with Majorana stars
• Winding-control mechanism of non-Hermitian systems