Nonunitary Scaling Theory of Non-Hermitian Localization

Abstract

Non-Hermiticity can destroy Anderson localization and lead to delocalization even in one dimension. However, the unified understanding of the non-Hermitian delocalization has yet to be established. Here, we develop a scaling theory of localization in non-Hermitian systems. We reveal that non-Hermiticity introduces a new scale and breaks down the one-parameter scaling, which is the central assumption of the conventional scaling theory of localization. Instead, we identify the origin of the unconventional non-Hermitian delocalization as the two-parameter scaling. Furthermore, we establish the threefold universality of non-Hermitian localization based on reciprocity; reciprocity forbids the delocalization without internal degrees of freedom, whereas symplectic reciprocity results in a new type of symmetry-protected delocalization.

arXiv comment6+14 pages, 2+2 figures, 1+1 tables

References in corpus (82)

• Random-Matrix Theory of Quantum Transport
• Nonreciprocal light transmission in parity-time-symmetric whispering-gallery microcavities
• Novel Symmetry Classes in Mesoscopic Normal-Superconducting Hybrid Structures
• Edge states and topological invariants of non-Hermitian systems
• Anderson Transitions
• Unidirectional Invisibility induced by PT-Symmetric Periodic Structures
• Anderson localization of a non-interacting Bose-Einstein condensate
• Exceptional Topology of Non-Hermitian Systems
• Direct observation of Anderson localization of matter-waves in a controlled disorder
• Localization transitions in non-Hermitian quantum mechanics
• Topological phases of non-Hermitian systems
• Symmetry and Topology in Non-Hermitian Physics
• Biorthogonal Bulk-Boundary Correspondence in Non-Hermitian Systems
• Topological Origin of Non-Hermitian Skin Effects
• Topological Band Theory for Non-Hermitian Hamiltonians
• Nonlinear waves in $\mathcal{P}\mathcal{T}$-symmetric systems
• Anomalous edge state in a non-Hermitian lattice
• Non-Bloch Band Theory of Non-Hermitian Systems
• Correspondence between winding numbers and skin modes in non-hermitian systems
• Lasing in topological edge states of a 1D lattice
• Visualization of Branch Points in PT-Symmetric Waveguides
• Non-Hermitian Chern bands
• Non-Hermitian Boundary Modes
• Spawning rings of exceptional points out of Dirac cones
• Anatomy of skin modes and topology in non-Hermitian systems
• Non-Hermitian robust edge states in one-dimension: Anomalous localization and eigenspace condensation at exceptional points
• Edge Modes, Degeneracies, and Topological Numbers in Non-Hermitian Systems
• Scaling Theory of the Integer Quantum Hall Effect
• Probing topological invariants in the bulk of a non-Hermitian optical system
• Vortex Pinning and Non-Hermitian Quantum Mechanics
• Observation of Bulk Fermi Arc and Polarization Half Charge from Paired Exceptional Points
• Selective enhancement of topologically induced interface states in a dielectric resonator chain
• Weyl Exceptional Rings in a Three-Dimensional Dissipative Cold Atomic Gas
• Edge states and topological phases in non-Hermitian systems
• Topological Transition in a Non-Hermitian Quantum Walk
• Anti-Parity-Time Symmetric Optics via Flying Atoms
• Topological phase transition in non-Hermitian quasicrystals
• Periodic Table for Topological Bands with Non-Hermitian Bernard-LeClair Symmetries
• Classification of Exceptional Points and Non-Hermitian Topological Semimetals
• Topologically protected midgap states in complex photonic lattices
• Interplay of non-Hermitian skin effects and Anderson localization in non-reciprocal quasiperiodic lattices
• Non-Hermitian Delocalization and Eigenfunctions
• Non-Hermitian Many-Body Localization
• Parity-time-symmetric quantum critical phenomena
• Random-matrix theory of Majorana fermions and topological superconductors
• Active topological photonics
• Robust light transport in non-Hermitian photonic lattices
• Topological unification of time-reversal and particle-hole symmetries in non-Hermitian physics
• Absence of topological insulator phases in non-Hermitian PT-symmetric Hamiltonians
• Non-Hermitian Localization and Population Biology
• Information Retrieval and Criticality in Parity-Time-Symmetric Systems
• Non-Hermitian systems and topology: A transfer-matrix perspective
• Non-Hermitean Random Matrix Theory: method of hermitization
• Phase-dependent chiral transport and effective non-Hermitian dynamics in a bosonic Kitaev-Majorana chain
• Observation of critical phenomena in parity-time-symmetric quantum dynamics
• Topological Phases in Non-Hermitian Aubry-André-Harper Models
• Random Network Models and Quantum Phase Transitions in Two Dimensions
• Non-Hermitian Kondo effect in ultracold alkaline-earth atoms
• Distribution of Eigenvalues in Non-Hermitian Anderson Model
• Directed Quantum Chaos
• Non-Hermitean Localization and De-Localization
• Topological Phase Transition driven by Infinitesimal Instability: Majorana Fermions in Non-Hermitian Spintronics
• Non-Hermitian disorder in two-dimensional optical lattices
• Non-Hermitian Topological Theory of Finite-Lifetime Quasiparticles: Prediction of Bulk Fermi Arc Due to Exceptional Point
• Universality classes of non-Hermitian random matrices
• Delocalization in coupled one-dimensional chains
• Delocalization Transition via Supersymmetry in one Dimension
• Anderson transition in three-dimensional systems with non-Hermitian disorder
• Constant-pressure sound waves in non-Hermitian disordered media
• Theory of directed localization in one dimension
• Probability of Reflection by a Random Laser
• Non-Hermitian Localization in Biological Networks
• Localization and delocalization in dirty superconducting wires
• Breakdown of the Mott insulator: Exact solution of an asymmetric Hubbard model
• Time-Reversal Symmetry in Non-Hermitian Systems
• Localization of Light: Dual Symmetry between Absorption and Amplification
• A Classification of Non-Hermitian Random Matrices
• The Kibble-Zurek mechanism at exceptional points
• Random Dirac Fermions and Non-Hermitian Quantum Mechanics
• Finite Size Scaling Analysis of the Anderson Transition
• Delocalization in an open one-dimensional chain in an imaginary vector potential
• Crossover of conductance and local density of states in a single-channel disordered quantum wire

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• Entanglement Phase Transition Induced by the Non-Hermitian Skin Effect
• Localization transition, spectrum structure and winding numbers for one-dimensional non-Hermitian quasicrystals
• Universality classes of the Anderson Transitions Driven by non-Hermitian Disorder
• Symmetry of Open Quantum Systems: Classification of Dissipative Quantum Chaos
• Non-Hermitian Topological Phases: Principles and Prospects
• Unifying the Anderson Transitions in Hermitian and Non-Hermitian Systems
• Dimensional transmutation from non-Hermiticity
• Transfer matrix study of the Anderson transition in non-Hermitian systems
• Non-Hermitian Floquet Topological Matter -- A Review
• Cascade of the delocalization transition in a non-Hermitian interpolating Aubry-Andr{é}-Fibonacci chain
• Nielsen-Ninomiya Theorem with Bulk Topology: Duality in Floquet and Non-Hermitian Systems
• Nonequilibrium dynamics of the localization-delocalization transition in the non-Hermitian Aubry-André model
• Non-Hermitian Rosenzweig-Porter random-matrix ensemble: Obstruction to the fractal phase
• Reentrant localization transition in the Su-Schrieffer-Heeger model with random-dimer disorder
• Quantum Entanglement of Non-Hermitian Quasicrystals
• Spectral rigidity of non-Hermitian symmetric random matrices near Anderson transition
• Diagnosing non-Hermitian Many-Body Localization and Quantum Chaos via Singular Value Decomposition
• Singular-Value Statistics of Non-Hermitian Random Matrices and Open Quantum Systems
• Level statistics of real eigenvalues in non-Hermitian systems
• Protection of parity-time symmetry in topological many-body systems: non-Hermitian toric code and fracton models
• Anderson localization transitions in disordered non-Hermitian systems with exceptional points
• Activity-induced phase transition in a quantum many-body system
• Universality classes of the Anderson transition in three-dimensional symmetry classes AIII, BDI, C, D and CI
• Entanglement dynamics in the many-body Hatano-Nelson model
• Non-Hermiticity induces localization: good and bad resonances in power-law random banded matrices
• Anderson Delocalization in Strongly Coupled Disordered Non-Hermitian Chains
• Phase transitions and bunching of correlated particles in a non-Hermitian quasicrystal
• Universal non-Hermitian transport in disordered systems
• Non-Hermitian Skin Effect in Periodically-Driven Dissipative Ultracold Atoms
• Damping transition in an open generalized Aubry-André-Harper model
• Statics and Dynamics of non-Hermitian Many-Body Localization
• Exponential size scaling of the Liouvillian gap in boundary-dissipated systems with Anderson localization
• Topological triple phase transition in non-Hermitian quasicrystals with complex asymmetric hopping
• Anderson localization versus hopping asymmetry in a disordered lattice
• Nonlinear Landauer formula: Nonlinear response theory of disordered and topological materials
• Field theory of non-Hermitian disordered systems
• Infernal and Exceptional Edge Modes: Non-Hermitian Topology Beyond the Skin Effect
• Robust quantum boomerang effect in non-Hermitian systems
• Metal-insulator transition in a 2D system of chiral unitary class
• Universal scaling of Green's functions in disordered non-Hermitian systems
• Ubiquity of the quantum boomerang effect in Hermitian Anderson-localized systems
• Localization-Delocalization Transitions in Non-Hermitian Aharonov-Bohm Cages
• Eigenvector Correlations Across the Localisation Transition in non-Hermitian Power-Law Banded Random Matrices
• Kibble-Zurek scaling in one-dimensional localization transitions
• Generalized multifractality in 2D disordered systems of chiral symmetry classes
• Dynamical localization transition in the non-Hermitian lattice gauge theory
• Scale-free localization versus Anderson localization in unidirectional quasiperiodic lattices
• Dynamical localization in non-Hermitian quasi-crystals
• Universal hard-edge statistics of non-Hermitian random matrices
• Anisotropic-scaling localization in higher-dimensional non-Hermitian systems
• Localization of Lindbladian Fermions
• Phase transitions of wave packet dynamics in disordered non-Hermitian systems
• Lack of near-sightedness principle in non-Hermitian systems
• Non-Hermitian off-diagonal disordered optical lattices
• Phase transitions in non-Hermitian superlattices
• Delocalization of interacting directed polymers on a periodic substrate: Localization length and critical exponents from non-Hermitian spectra
• Eigenvalue spectral tails and localization properties of asymmetric networks
• Two-body interaction induced phase transitions and intermediate phases in nonreciprocal non-Hermitian quasicrystals
• Continuous phase transition induced by non-Hermiticity in the quantum contact process model
• Interplay of Disorder and Point-Gap Topology: Chiral Modes, Localization and Non-Hermitian Anderson Skin Effect in One Dimension
• Scaling behavior of the localization length for TE waves at critical incidence on short-range correlated stratified random media
• Dynamical transition in non-Hermitian Chern insulator
• Arbitrary Control of Non-Hermitian Skin Modes via Disorder and An Electric Field
• Physical relevance of time-independent scattering calculations in non-Hermitian systems: The role of time-growing bound states
• Supermetal-insulator transition in a non-Hermitian network model
• Theory of the Anderson transition in three-dimensional chiral symmetry classes: Connection to type-II superconductors
• Winding-control mechanism of non-Hermitian systems
• Non-linear sigma models for non-Hermitian random matrices in symmetry classes AI${}^{†}$ and AII${}^{†}$
• Localization with non-Hermitian off-diagonal disorder
• Correspondence between non-Hermitian topology and directional amplification in the presence of disorder