General criterion for non-Hermitian skin effects and Application: Fock space skin effects in many body systems

Abstract

Non-Hermiticity enables macroscopic accumulation of bulk states, named non-Hermitian skin effects. The non-Hermitian skin effects are well-established for single-particle systems, but their proper characterization for general systems is elusive. Here, we propose a general criterion of non-Hermitian skin effects, which works for any finite-dimensional system evolved by a linear operator. The applicable systems include many-body systems and network systems. A system meeting the criterion exhibits enhanced non-normality of the evolution operator, accompanied by exceptional characteristics intrinsic to non-Hermitian systems. Applying the criterion, we discover a new type of non-Hermitian skin effect in many-body systems, which we dub the Fock space skin effect. We also discuss the Fock space skin effect-induced slow dynamics, which gives an experimental signal for the Fock space skin effect.

arXiv comment7+10 pages, 4+3 figures

References in corpus (89)

• Real Spectra in Non-Hermitian Hamiltonians Having PT Symmetry
• Making Sense of Non-Hermitian Hamiltonians
• Edge states and topological invariants of non-Hermitian systems
• Anderson Transitions
• Complex Extension of Quantum Mechanics
• A High Phase-Space-Density Gas of Polar Molecules
• Exceptional Topology of Non-Hermitian Systems
• Non-Hermitian Physics
• A quantum gas microscope - detecting single atoms in a Hubbard regime optical lattice
• 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
• Non-Hermitian Chern bands
• Non-Hermitian Boundary Modes
• Spawning rings of exceptional points out of Dirac cones
• Observation of non-Hermitian bulk-boundary correspondence in quantum dynamics
• Efficient Light Funneling based on the non-Hermitian Skin Effect
• Anatomy of skin modes and topology in non-Hermitian systems
• Non-Hermitian robust edge states in one-dimension: Anomalous localization and eigenspace condensation at exceptional points
• 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
• Non-Hermitian skin effect and chiral damping in open quantum systems
• Observation of non-Hermitian topology and its bulk-edge correspondence in an active mechanical metamaterial
• Selective enhancement of topologically induced interface states in a dielectric resonator chain
• Ultracold Dipolar Gas of Fermionic ${}^{23}$Na${}^{40}$K Molecules in their Absolute Ground State
• Edge states and topological phases in non-Hermitian systems
• Non-reciprocal robotic metamaterials
• Topological Transition in a Non-Hermitian Quantum Walk
• Critical non-Hermitian Skin Effect
• Quantum degenerate dipolar Fermi gas
• Universal non-Hermitian skin effect in two and higher dimensions
• Non-Hermitian Topological Sensors
• Classification of Exceptional Points and Non-Hermitian Topological Semimetals
• Reciprocal skin effect and its realization in a topolectrical circuit
• Topologically protected midgap states in complex photonic lattices
• Observation of Non-Hermitian Skin Effect and Topology in Ultracold Atoms
• Non-Hermitian topological phenomena: A review
• Higher-order non-Hermitian skin effect
• Topological Non-Hermitian skin effect
• Non-Hermitian Many-Body Localization
• Absence of topological insulator phases in non-Hermitian PT-symmetric Hamiltonians
• Non-Hermitian extensions of higher-order topological phases and their biorthogonal bulk-boundary correspondence
• Long-lived dipolar molecules and Feshbach molecules in a 3D optical lattice
• Non-Bloch band theory of non-Hermitian Hamiltonians in the symplectic class
• Creation of a low-entropy quantum gas of polar molecules in an optical lattice
• Second-order topological non-Hermitian skin effects
• Liouvillian Skin Effect: Slowing Down of Relaxation Processes without Gap Closing
• Topological Phase Transition driven by Infinitesimal Instability: Majorana Fermions in Non-Hermitian Spintronics
• Skin superfluid, topological Mott insulators, and asymmetric dynamics in interacting non-Hermitian Aubry-Andre-Harper models
• Non-Hermitian second-order skin and topological modes
• Mirror skin effect and its electric circuit simulation
• Emergent Fermi surface in a many-body non-Hermitian Fermionic chain
• Many-body topology of non-Hermitian systems
• Many-body approach to non-Hermitian physics in fermionic systems
• Symmetry breaking and spectral structure of the interacting Hatano-Nelson model
• Resolving Discrepancy between Liouvillian Gap and Relaxation Time in Boundary-Dissipated Quantum Many-Body Systems
• Many-Body Topological and Skin States without Open Boundaries
• Non-Hermitian Many-Body Localization with Open Boundaries
• Time-Reversal Symmetry in Non-Hermitian Systems
• Liouvillian Skin Effect in an Exactly Solvable Model
• Fate of the non-Hermitian skin effect in many-body fermionic systems
• Hermitian zero modes protected by nonnormality: Application of pseudospectra
• Interaction-induced non-Hermitian topological phases from a dynamical gauge field
• Non-Hermitian Mott Skin Effect
• Observation of non-Hermitian topology in a multi-terminal quantum Hall device
• Non-Hermitian skin effect in one-dimensional interacting Bose gas
• Exact solution of the Bose Hubbard model with unidirectional hopping
• Many-body non-Hermitian skin effect under dynamic gauge coupling
• Topological enhancement of non-normality in non-Hermitian skin effects
• Interaction-induced Liouvillian skin effect in a fermionic chain with a two-body loss
• A brief review of hybrid skin-topological effect
• Scale-free non-Hermitian skin effect in a boundary-dissipated spin chain
• Phase transitions and bunching of correlated particles in a non-Hermitian quasicrystal
• Emergent Mott insulators and non-Hermitian conservation laws in an interacting bosonic chain with noninteger filling and nonreciprocal hopping
• Full counting statistics in the many-body Hatano-Nelson model
• Quantum criticality in interacting bosonic Kitaev-Hubbard models
• Many-body Non-Hermitian Skin Effect At Finite Temperatures
• From Ergodicity to Many-Body Localization in a One-Dimensional Interacting Non-Hermitian Stark System
• Boundary sensitive Lindbladians and relaxation dynamics
• Bulk-Edge Correspondence for Point-Gap Topological Phases in Junction Systems

Cited by in corpus (17)

• Erratic non-Hermitian skin localization
• The non-Hermitian skin effect: A perspective
• Multifractality of many-body non-Hermitian skin effect
• Numerical instability of non-Hermitian Hamiltonian evolutions
• Quasiperiodicity-induced bulk localization with self similarity in non-Hermitian systems
• Anisotropic-scaling localization in higher-dimensional non-Hermitian systems
• Many-Body Non-Hermitian Skin Effect with Exact Steady States in the Dissipative Quantum Link Model
• Non-Hermitian ultra-strong bosonic clustering through interaction-induced caging
• Non-Hermitian skin effect in fragmented Hilbert spaces of one-dimensional fermionic lattices
• Exceptional second-order topological insulators
• Unified Bulk-Entanglement Correspondence in Non-Hermitian Systems
• Multifractal statistics of non-Hermitian skin effect on the Cayley tree
• Magnetic Control of the Non-Hermitian Skin Effect in Two-Dimensional Lattices
• Emergence of non-trivial phases in interacting non-Hermitian quasiperiodic chains with power-law hopping
• Liouvillian skin effects in two-dimensional electron systems at finite temperatures
• Interacting many-body non-Hermitian systems as Markov chains
• Winding-control mechanism of non-Hermitian systems