Non-Hermitian skin effect and self-acceleration

Abstract

Non-Hermitian systems exhibit nontrivial band topology and a strong sensitivity of the energy spectrum on the boundary conditions. Remarkably, a macroscopic number of bulk states get squeezed toward the lattice edges under open boundary conditions, an effect dubbed the non-Hermitian skin effect (NHSE). A well-established dynamical signature of the NHSE in real space is the directional bulk flow (or persistent current) for arbitrary initial excitation of the system, which is observed at long times. Here we unravel a different dynamical signature of the NHSE in real space that manifests itself in the {\em early-time} dynamics of the system, namely self-acceleration of the wave function. Self-acceleration is demonstrated to occur rather generally in single--band lattice models probed by single-site excitation, where the acceleration turns out to be proportional to the area enclosed by the energy spectrum of the Bloch Hamiltonian under periodic boundary conditions. The observation of wave packet self-acceleration at early times is a clear signature of the NHSE and should be experimentally accessible using synthetic non-Hermitian matter, for example in discrete-time photonic quantum walks.

13 pages, 4 figures, accepted for publication in the Physical Review B

References in corpus (45)

• Topological Origin of Non-Hermitian Skin Effects
• Efficient Light Funneling based on the non-Hermitian Skin Effect
• Edge Modes, Degeneracies, and Topological Numbers in Non-Hermitian Systems
• Topological phase transition in non-Hermitian quasicrystals
• Periodic Table for Topological Bands with Non-Hermitian Bernard-LeClair Symmetries
• Universal non-Hermitian skin effect in two and higher dimensions
• Higher-order non-Hermitian skin effect
• New topological invariants in non-Hermitian systems
• Observation of arbitrary topological windings of a non-Hermitian band
• Exact solution of non-Hermitian systems with generalized boundary conditions: size-dependent boundary effect and fragility of skin effect
• Defining a bulk-edge correspondence for non-Hermitian Hamiltonians via singular-value decomposition
• Second-order topological non-Hermitian skin effects
• Observation of non-Hermitian topological Anderson insulator in quantum dynamics
• Skin effect and winding number in disordered non-Hermitian systems
• Non-Hermitian Edge Burst
• Localization transition, spectrum structure and winding numbers for one-dimensional non-Hermitian quasicrystals
• Exact mobility edges, $\mathcal{P}\mathcal{T}$-symmetry breaking and skin effect in one-dimensional non-Hermitian quasicrystals
• Observation of Bloch oscillations in complex PT-symmetric photonic lattices
• Phase transitions in a non-Hermitian Aubry-André-Harper model
• Non-Hermitian Floquet topological phases: Exceptional points, coalescent edge modes, and the skin effect
• Non-Hermitian second-order skin and topological modes
• Unraveling the Non-Hermitian Skin Effect in Dissipative Systems
• Non-Hermitian Skin Effects in Hermitian Correlated/Disordered Systems: Boundary-Sensitive/Insensitive Quantities and Pseudo Quantum Number
• Quantum anomaly, non-Hermitian skin effects, and entanglement entropy in open systems
• Boundary-dependent Self-dualities, Winding Numbers and Asymmetrical Localization in non-Hermitian Quasicrystals
• Exceptional Bound States and negative Entanglement Entropy
• Exact non-Hermitian mobility edges in one-dimensional quasicrystal lattice with exponentially decaying hopping and its dual lattice
• Non-Bloch band theory in bosonic Bogoliubov-de Gennes systems
• Anomalous topological edge states in non-Hermitian piezophononic media
• Magnetic suppression of non-Hermitian skin effects
• Detecting non-Bloch topological invariants in quantum dynamics
• Non-Hermitian skin effect beyond the tight-binding models
• Non-Hermitian band topology with generalized inversion symmetry
• Non-Hermitian skin effect of dislocations and its topological origin
• Non-Hermitian topological phases and dynamical quantum phase transitions: A generic connection
• Connections between the Open-boundary Spectrum and Generalized Brillouin Zone in Non-Hermitian Systems
• Non-Hermitian Maryland Model
• Non-Bloch quench dynamics
• Always-Real-Eigenvalued Non-Hermitian Topological Systems
• Topological delocalization transitions and mobility edges in the nonreciprocal Maryland model
• Quantum transport in a one-dimensional quasicrystal with mobility edges
• Non-Hermitian topological phase transitions in superlattices and the optical Dirac equation
• Selective and tunable excitation of topological non-Hermitian skin modes
• Scaling rule in critical non-Hermitian skin effect
• Self-healing of non-Hermitian topological skin modes

Cited by in corpus (40)

• Topological Non-Hermitian skin effect
• Non-Hermitian Topological Phases: Principles and Prospects
• Non-Bloch bands in two-dimensional non-Hermitian systems
• Anatomy of open-boundary bulk in multiband non-Hermitian systems
• Generalized Quantum Geometric Tensor in a Non-Hermitian Exciton-Polariton System
• Green's functions of multiband non-Hermitian systems
• Phase transitions and bunching of correlated particles in a non-Hermitian quasicrystal
• The non-Hermitian skin effect: A perspective
• Self acceleration from spectral geometry in dissipative quantum-walk dynamics
• Hybrid scale-free skin effect in non-Hermitian systems: A transfer matrix approach
• Steady-state edge burst: From free-particle systems to interaction-induced phenomena
• Anderson localization versus hopping asymmetry in a disordered lattice
• Nontrivial worldline winding in non-Hermitian quantum systems
• Exact non-Hermitian mobility edges and robust flat bands in two-dimensional Lieb lattices with imaginary quasiperiodic potentials
• Non-Hermitian skin effect enforced by nonsymmorphic symmetries
• Invisible non-Hermitian potentials in discrete-time photonic quantum walks
• Non-Hermitian invisibility in tight-binding lattices
• Nonlinear flip-flop quantum walks through potential barriers
• Self-trapping and skin solitons in two-dimensional non-Hermitian lattices
• General theory for infernal points in non-Hermitian systems
• Localization and mobility edges in non-Hermitian continuous quasiperiodic systems
• Harnessing Nonlinearity to Tame Wave Dynamics in Nonreciprocal Active Systems
• Non-reciprocity is necessary for robust dimensional reduction and strong responses in stochastic topological systems
• Real-time edge dynamics of non-Hermitian lattices
• Optical pumping through the Liouvillian skin effect
• Exceptional second-order topological insulators
• Antichiral and trap-skin dynamics in a nonreciprocal bosonic two-leg ladder with artificial magnetic flux
• Phase transitions in non-Hermitian superlattices
• Defect-driven incoherent skin localization
• Apodized photonic crystals: A non-dissipative system hosting multiple exceptional points
• Unified Bulk-Entanglement Correspondence in Non-Hermitian Systems
• Solution of Wave Acceleration and Non-Hermitian Jump in Nonreciprocal Lattices
• Origin of Robust ${\mathbb{Z}}_2$ Topological Phases in Stacked Hermitian Systems: Non-Hermitian Level Repulsion
• Higher-order Topological Knots and the classification of non-Hermitian lattices under $C_n$ symmetry
• Size-Dependent Skin Effect Transitions in Weakly Coupled Non-Reciprocal Chains
• Optimal spectral transport of non-Hermitian systems
• Critical properties in the non-Hermitian Aubry-Andre-Stark model
• Wiener-Hopf factorization and non-Hermitian topology for Amoeba formulation in one-dimensional multiband systems
• Insensitive nonreciprocal edge breathers
• Generic non-Hermitian mobility edges in a class of duality-breaking quasicrystals