Boundary-dependent Self-dualities, Winding Numbers and Asymmetrical Localization in non-Hermitian Quasicrystals

Abstract

We study a non-Hermitian Aubry-André-Harper model with both nonreciprocal hoppings and complex quasiperiodical potentials, which is a typical non-Hermitian quasicrystal. We introduce boundary-dependent self-dualities in this model and obtain analytical results to describe its Asymmetrical Anderson localization and topological phase transitions. We find that the Anderson localization is not necessarily in accordance with the topological phase transitions, which are characteristics of localization of states and topology of energy spectrum respectively. Furthermore, in the localized phase, single-particle states are asymmetrically localized due to non-Hermitian skin effect and have energy-independent localization lengths. We also discuss possible experimental detections of our results in electric circuits.

6 pages, 3 figures

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Cited by in corpus (42)

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• Phase transitions in a non-Hermitian Aubry-André-Harper model
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• Exact non-Hermitian mobility edges in one-dimensional quasicrystal lattice with exponentially decaying hopping and its dual lattice
• Non-Hermitian skin effect beyond the tight-binding models
• Dimerization induced mobility edges and multiple reentrant localization transitions in non-Hermitian quasicrystals
• Cascade of the delocalization transition in a non-Hermitian interpolating Aubry-Andr{é}-Fibonacci chain
• Floquet engineering of topological localization transitions and mobility edges in one-dimensional non-Hermitian quasicrystals
• Anderson localization and topological phase transitions in non-Hermitian Aubry-André-Harper models with p-wave pairing
• Nonequilibrium dynamics of the localization-delocalization transition in the non-Hermitian Aubry-André model
• Topological Anderson insulators with different bulk states in quasiperiodic chains
• Quantum Entanglement of Non-Hermitian Quasicrystals
• Localization, $\mathcal{P}\mathcal{T}$-Symmetry Breaking and Topological Transitions in non-Hermitian Quasicrystals
• Non-Hermitian Maryland Model
• Driving-induced multiple $\mathcal{P}\mathcal{T}$-symmetry breaking transitions and reentrant localization transitions in non-Hermitian Floquet quasicrystals
• Entanglement phase transitions in non-Hermitian quasicrystals
• Non-Abelian generalization of non-Hermitian quasicrystal: PT-symmetry breaking, localization, entanglement and topological transitions
• Non-Hermitian butterfly spectra in a family of quasiperiodic lattices
• Phase transitions and bunching of correlated particles in a non-Hermitian quasicrystal
• Topological delocalization transitions and mobility edges in the nonreciprocal Maryland model
• Asymmetric transfer matrix analysis of Lyapunov exponents in one-dimensional non-reciprocal quasicrystals
• Non-Hermitian topological mobility edges and transport in photonic quantum walks
• Filling up complex spectral regions through non-Hermitian disordered chains
• Non-Hermitian edge burst without skin localizations
• Hybrid scaling properties of localization transition in a non-Hermitian disorder Aubry-André model
• Exact complex mobility edges and flagellate spectra for non-Hermitian quasicrystals with exponential hoppings
• Correlation-induced phase transitions and mobility edges in an interacting non-Hermitian quasicrystal
• Topological phonon polariton enhanced radiative heat transfer in bichromatic nanoparticle arrays mimicking Aubry-André-Harper model
• From scale-free to Anderson localization: a size-dependent transition
• Robust Anderson transition in non-Hermitian photonic quasicrystals
• Scale-free localization versus Anderson localization in unidirectional quasiperiodic lattices
• General mapping of one-dimensional non-Hermitian mosaic models to non-mosaic counterparts: Mobility edges and Lyapunov exponents
• Emergent multi-loop nested point gap in a non-Hermitian quasiperiodic lattice
• Multifractal-enriched mobility edges and emergent quantum phases in Rydberg atomic arrays
• Localization and topological transitions in generalized non-Hermitian SSH models
• Bose-Einstein condensation processes with nontrivial geometric multiplicites realized via $\mathcal{P}\mathcal{T}-$symmetric and exactly solvable linear-Bose-Hubbard building blocks
• Exact mobility line and mobility ring in the complex energy plane of a flat band lattice with a non-Hermitian quasiperiodic potential
• Anderson-skin dualism: A boundary-dependent effect in non-Hermitian disordered coupled systems
• Two-body interaction induced phase transitions and intermediate phases in nonreciprocal non-Hermitian quasicrystals
• Coexistence of extended and localized states in one-dimensional non-Hermitian Anderson model
• Arithmetic Tuning of Dynamical Critical Exponents in Quasiperiodic Localization Transitions