Localization transition, spectrum structure and winding numbers for one-dimensional non-Hermitian quasicrystals

Abstract

By analyzing the Lyapunov exponent (LE), we develop a rigorous, fundamental scheme for the study of general non-Hermitian quasicrystals with both complex phase factor and non-reciprocal hopping. Specially, the localization-delocalization transition point, $\mathcal{P}\mathcal{T}$-symmetry-breaking point and the winding number transition points are determined by LEs of its dual Hermitian model. The analysis was based on Avila's global theory, and we found that winding number is directly related to the acceleration, the slope of the LE, while quantization of acceleration is the crucial ingredient of Avila's global theory. This result applies as well to the models with higher winding, not only the simplest Aubry-André model. As typical examples, we obtain the analytical phase boundaries of localization transition for non-Hermitian Aubry-André model in the whole parameter space, and the complete phase diagram is straightforwardly determined. For the non-Hermitian Soukoulis-Economou model, a high winding model, we show how the phase boundaries of localization transition and winding number transitions relate to the LEs of its dual Hermitian model. Moreover, we discover an intriguing feature of robust spectrum, i.e., the spectrum keeps invariant when one changes the complex phase parameter $h$ or non-reciprocal parameter $g$ in the region of $h<|h_c|$ or $g<|g_c|$ if the system is in the extended or localized state, respectively.

17 pages, 10 figures. version to appear in Phys. Rev. B

References in corpus (24)

• Anderson Transitions
• Topological Origin of Non-Hermitian Skin Effects
• Efficient Light Funneling based on the non-Hermitian Skin Effect
• Topological phase transition in non-Hermitian quasicrystals
• Periodic Table for Topological Bands with Non-Hermitian Bernard-LeClair Symmetries
• Nearest neighbor tight binding models with an exact mobility edge in one dimension
• One dimensional quasiperiodic mosaic lattice with exact mobility edges
• Localization in one dimensional lattices with non-nearest-neighbor hopping: Generalized Anderson and Aubry-André models
• Localization and adiabatic pumping in a generalized Aubry-André-Harper model
• Skin effect and winding number in disordered non-Hermitian systems
• 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
• Nonunitary Scaling Theory of Non-Hermitian Localization
• Anderson transition in three-dimensional systems with non-Hermitian disorder
• Many-body localization in a non-Hermitian quasi-periodic system
• Phase transitions in a non-Hermitian Aubry-André-Harper model
• Localization and topological transitions in non-Hermitian quasiperiodic lattices
• Universality classes of the Anderson Transitions Driven by non-Hermitian Disorder
• Boundary-dependent Self-dualities, Winding Numbers and Asymmetrical Localization in non-Hermitian Quasicrystals
• Exact non-Hermitian mobility edges in one-dimensional quasicrystal lattice with exponentially decaying hopping and its dual lattice
• Topological Anderson insulators in two-dimensional non-Hermitian disordered systems
• Anderson localization and topological phase transitions in non-Hermitian Aubry-André-Harper models with p-wave pairing
• Non-Hermitian spectra and Anderson localization
• Localization problem of the quasiperiodic system with the spin orbit interaction

Cited by in corpus (86)

• Topological Non-Hermitian skin effect
• Simulating non-Hermitian quasicrystals with single-photon quantum walks
• Phase transitions in a non-Hermitian Aubry-André-Harper model
• Non-Hermitian skin effect and self-acceleration
• Anomalous Skin Effects in Disordered Systems with a Single non-Hermitian Impurity
• Exact non-Hermitian mobility edges in one-dimensional quasicrystal lattice with exponentially decaying hopping and its dual lattice
• Non-Hermitian Topological Phases: Principles and Prospects
• Critical phase dualities in 1D exactly-solvable quasiperiodic models
• Dimerization induced mobility edges and multiple reentrant localization transitions in non-Hermitian quasicrystals
• Spectral deformations in non-Hermitian lattices with disorder and skin effect: a solvable model
• Nonequilibrium dynamics of the localization-delocalization transition in the non-Hermitian Aubry-André model
• Bulk-Bulk Correspondence in Disordered Non-Hermitian Systems
• Non-Hermitian Aubry-André model with Power-Law Hopping
• Quantum Entanglement of Non-Hermitian Quasicrystals
• Hybrid skin-topological effect induced by eight-site cells and arbitrary adjustment of the localization of topological edge states
• Properties of the non-Hermitian SSH model: role of PT-symmetry
• Localization, $\mathcal{P}\mathcal{T}$-Symmetry Breaking and Topological Transitions in non-Hermitian Quasicrystals
• Non-Hermitian Maryland Model
• Many-body non-Hermitian skin effect under dynamic gauge coupling
• Entanglement phase transitions in non-Hermitian quasicrystals
• Exact Mobility Edges and Topological Phase Transition in Two-Dimensional non-Hermitian Quasicrystals
• Non-Hermitian skin effect edge
• Non-Abelian generalization of non-Hermitian quasicrystal: PT-symmetry breaking, localization, entanglement and topological transitions
• Generic mobility edges in several classes of duality-breaking one-dimensional quasiperiodic potentials
• Multiple localization transitions and novel quantum phases induced by staggered on-site potential
• Non-Hermitian butterfly spectra in a family of quasiperiodic lattices
• Engineering Dissipative Quasicrystals
• Topological delocalization transitions and mobility edges in the nonreciprocal Maryland model
• Phase transitions and bunching of correlated particles in a non-Hermitian quasicrystal
• Emergence of multifractality through cascade-like transitions in a mosaic interpolating Aubry-André-Fibonacci chain
• Universal non-Hermitian transport in disordered systems
• Engineering mobility in quasiperiodic lattices with exact mobility edges
• Damping transition in an open generalized Aubry-André-Harper model
• Asymmetric transfer matrix analysis of Lyapunov exponents in one-dimensional non-reciprocal quasicrystals
• Topological triple phase transition in non-Hermitian quasicrystals with complex asymmetric hopping
• Quantum criticality in the disordered Aubry-André model
• Exponential size scaling of the Liouvillian gap in boundary-dissipated systems with Anderson localization
• Non-Hermitian topological mobility edges and transport in photonic quantum walks
• Non-Hermitian topology and criticality in photonic arrays with engineered losses
• Non-Hermitian edge burst without skin localizations
• The simulation of non-Hermitian disordered system in linear circuits
• Exact complex mobility edges and flagellate spectra for non-Hermitian quasicrystals with exponential hoppings
• Universal scaling of Green's functions in disordered non-Hermitian systems
• Evolution of spectral topology in one-dimensional long-range nonreciprocal lattices
• Correlation-induced phase transitions and mobility edges in an interacting non-Hermitian quasicrystal
• Kibble-Zurek scaling in one-dimensional localization transitions
• Quantum-Classical Correspondence of Non-Hermitian Symmetry Breaking
• Exact non-Hermitian mobility edges and robust flat bands in two-dimensional Lieb lattices with imaginary quasiperiodic potentials
• Detecting bulk and edge exceptional points in non-Hermitian systems through generalized Petermann factors
• Equivalence and superposition of real and imaginary quasiperiodicities
• Engineering imaginary stark ladder in a dissipative lattice: passive $\mathcal{P}\mathcal{T}$ symmetry, K symmetry and localized damping
• General mapping of one-dimensional non-Hermitian mosaic models to non-mosaic counterparts: Mobility edges and Lyapunov exponents
• Scale-free localization versus Anderson localization in unidirectional quasiperiodic lattices
• Emergent multi-loop nested point gap in a non-Hermitian quasiperiodic lattice
• Quasiperiodicity-induced bulk localization with self similarity in non-Hermitian systems
• Multifractal-enriched mobility edges and emergent quantum phases in Rydberg atomic arrays
• Dynamical localization in non-Hermitian quasi-crystals
• Wannier-Stark localization in one-dimensional amplitude-chirped lattices
• Coexistence of non-Hermitian skin effect and extended states in one-dimensional nonreciprocal lattices
• Controlled probing of localization effects in the non-Hermitian Aubry-André model via topolectrical circuits
• Localization and topological transitions in generalized non-Hermitian SSH models
• Localization and mobility edges in non-Hermitian continuous quasiperiodic systems
• Phase Transitions in Quasi-Periodically Driven Quantum Critical Systems: Analytical Results
• Anomalous spectrum in a non-Hermitian quasiperiodic chain
• Extended-localized transition in diffusive quasicrystals
• Topology and its detection in a dissipative Aharonov-Bohm chain
• Exact mobility line and mobility ring in the complex energy plane of a flat band lattice with a non-Hermitian quasiperiodic potential
• Non-Hermitian off-diagonal disordered optical lattices
• Phase transitions in non-Hermitian superlattices
• Two-body interaction induced phase transitions and intermediate phases in nonreciprocal non-Hermitian quasicrystals
• Non-Hermitian Delocalization Induced by Residue Imaginary Velocity
• Exact multiple complex mobility edges and quantum state engineering in coupled 1D quasicystals
• Anderson-skin dualism: A boundary-dependent effect in non-Hermitian disordered coupled systems
• Convection-modulated topological edge mode and extended-localized criticality in thermal metamaterials
• Dissolution of the non-Hermitian skin effect in one-dimensional lattices with linearly varying nonreciprocal hopping
• Generalized Aubry-André-Harper model with power-law quasiperiodic potentials
• Real spectra and phase transition of skin effect in nonreciprocal systems
• Family of self-dual quasicrystals with critical Phases
• Gaussian eigenstate pinning in non-Hermitian quantum mechanics
• Coexistence of extended and localized states in one-dimensional non-Hermitian Anderson model
• Magnetic Control of the Non-Hermitian Skin Effect in Two-Dimensional Lattices
• Optimal spectral transport of non-Hermitian systems
• Winding-control mechanism of non-Hermitian systems
• Theory of the Anderson transition in three-dimensional chiral symmetry classes: Connection to type-II superconductors
• Generic non-Hermitian mobility edges in a class of duality-breaking quasicrystals
• Physical relevance of time-independent scattering calculations in non-Hermitian systems: The role of time-growing bound states