Cascade of the delocalization transition in a non-Hermitian interpolating Aubry-Andr{é}-Fibonacci chain

Abstract

In this paper, the interplay of the non-Herimiticity and the cascade of delocalization transition in the quasi-periodic chain is studied. The study is applied in a non-Hermitian interpolating Aubry-Andr{é}-Fibonacci (IAAF) model, which combines the non-Hermitian Aubry-Andr{é} (AA) model and the non-Hermitian Fibonacci model through a varying parameter, and the non-Hermiticity in this model is introduced by the non-reciprocal hopping. In the non-Hermitian AA limit, the system undergoes a delocalization transition by tuning the potential strength. At the critical point, the spatial distribution of the critical state shows a self-similar structure with the relative distance between the peaks being the Fibonacci sequence, and the finite-size scaling of the inverse participation ratios $(\mathrm{IPRs})$ of the critical ground state with lattice size $L$ shows that ${\mathrm{IPR}}_g\propto L^{-0.1189}$. In the non-Hermitian Fibonacci limit, we find that the system is always in the extended phase. Along the continuous deformation from the non-Hermitian AA model into the non-Hermitian Fibonacci model in the IAAF model, the cascade of the delocalization transition is found, but only a few plateaux appear. Moreover, the self-similar structure of spatial distribution for the critical modes along the cascade transition is also found. In addition, we find that the delocalization transition and the real-complex transition for the excited states happen at almost the same parameter. Our results show that the non-Hermiticity provides an additional knob to control the cascade of the delocalization transition besides the on-site potential.

References in corpus (66)

• Real Spectra in Non-Hermitian Hamiltonians Having PT Symmetry
• Making Sense of Non-Hermitian Hamiltonians
• Edge states and topological invariants of non-Hermitian systems
• Localization transitions in non-Hermitian quantum mechanics
• Topological phases of non-Hermitian systems
• Biorthogonal Bulk-Boundary Correspondence in Non-Hermitian Systems
• Topological Origin of Non-Hermitian Skin Effects
• Topological States and Adiabatic Pumping in Quasicrystals
• Correspondence between winding numbers and skin modes in non-hermitian systems
• Non-Hermitian Chern bands
• Non-Hermitian Boundary Modes
• Non-Hermitian robust edge states in one-dimension: Anomalous localization and eigenspace condensation at exceptional points
• Vortex Pinning and Non-Hermitian Quantum Mechanics
• Non-Hermitian skin effect and chiral damping in open quantum systems
• Non-Hermitian bulk-boundary correspondence and auxiliary generalized Brillouin zone theory
• Weyl Exceptional Rings in a Three-Dimensional Dissipative Cold Atomic Gas
• Critical non-Hermitian Skin Effect
• Direct observation of a localization transition in quasi-periodic photonic lattices
• Topological phase transition in non-Hermitian quasicrystals
• Classification of Exceptional Points and Non-Hermitian Topological Semimetals
• Observation of Topological Phase Transitions in Photonic Quasicrystals
• The emergence, coalescence and topological properties of multiple exceptional points and their experimental realization
• Higher-order non-Hermitian skin effect
• Interplay of non-Hermitian skin effects and Anderson localization in non-reciprocal quasiperiodic lattices
• Non-Hermitian skin modes induced by on-site dissipations and chiral tunneling effect
• Non-Hermitian Delocalization and Eigenfunctions
• Non-Hermitian Many-Body Localization
• Topological Zero-Energy Modes in Gapless Commensurate Aubry-André-Harper Models
• Topological Equivalence between the Fibonacci Quasicrystal and the Harper Model
• Non-Hermitian perspective of the band structure in heavy-fermion systems
• Fluctuations of the inverse participation ratio at the Anderson transition
• Topological Phases in Non-Hermitian Aubry-André-Harper Models
• Critical Behavior and Fractality in Shallow One-Dimensional Quasiperiodic Potentials
• Metal-insulator phase transition in a non-Hermitian Aubry-André-Harper Model
• Non-Hermitean Localization and De-Localization
• Emergence of criticality through a cascade of delocalization transitions in quasiperiodic chains
• Winding Numbers and Generalized Mobility Edges in Non-Hermitian Systems
• Exact mobility edges, $\mathcal{P}\mathcal{T}$-symmetry breaking and skin effect in one-dimensional non-Hermitian quasicrystals
• Universality classes of non-Hermitian random matrices
• 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
• Mirror skin effect and its electric circuit simulation
• Non-Hermitian second-order skin and topological modes
• Localization and topological transitions in non-Hermitian quasiperiodic lattices
• Unraveling the Non-Hermitian Skin Effect in Dissipative Systems
• Flat bands in lattices with non-Hermitian coupling
• Boundary-dependent Self-dualities, Winding Numbers and Asymmetrical Localization in non-Hermitian Quasicrystals
• Butterfly effect in interacting Aubry-Andre model: thermalization, slow scrambling, and many-body localization
• Localization of interacting fermions in the Aubry-Andre' model
• Localization Transition in Incommensurate non-Hermitian Systems
• Critical eigenstates and their properties in one and two dimensional quasicrystals
• The Kibble-Zurek mechanism at exceptional points
• Kibble-Zurek mechanism with a single particle: dynamics of the localization-delocalization transition in the Aubry-André model
• Universality and Quantum Criticality in Quasiperiodic Spin Chains
• Dynamical evolution in a one-dimensional incommensurate lattice with $\mathcal{P}\mathcal{T}$ symmetry
• Kibble-Zurek scaling in the Yang-Lee edge singularity
• Non-Hermitian phase transition and eigenstate localization induced by asymmetric coupling
• Spectral rigidity of non-Hermitian symmetric random matrices near Anderson transition
• Anderson localization transition in a robust $\mathcal{P}\mathcal{T}$-symmetric phase of a generalized Aubry-Andre model
• Localization-delocalization transition in disordered systems with a direction
• Out-of-time-ordered correlator in non-Hermitian quantum systems
• Hybridized Kibble-Zurek scaling in the driven critical dynamics across an overlapping critical region
• Critical generalized inverse participation ratio distributions
• Anomalous Spontaneous Symmetry Breaking in non-Hermitian Systems with Biorthogonal Z2-symmetry
• Controlling wave-front shape and propagation time with tunable disordered non-Hermitian multilayers

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• Floquet engineering of topological localization transitions and mobility edges in one-dimensional non-Hermitian quasicrystals
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• Non-Abelian generalization of non-Hermitian quasicrystal: PT-symmetry breaking, localization, entanglement and topological transitions
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• Emergent strength-dependent scale-free mobility edge in a non-reciprocal long-range Aubry-André-Harper model
• Hybrid scaling properties of localization transition in a non-Hermitian disorder Aubry-André model
• Kibble-Zurek scaling in one-dimensional localization transitions
• Correlation-induced phase transitions and mobility edges in an interacting non-Hermitian quasicrystal
• Hidden self-duality and exact mobility edges in quasiperiodic network models
• Multiple intermediate phases in the interpolating Aubry-André-Fibonacci model
• Non-equilibrium dynamics of localization phase transition in the non-Hermitian Disorder-Aubry-André model
• Phase transitions in non-Hermitian superlattices
• Generalized Aubry-André-Harper model with power-law quasiperiodic potentials
• Coexistence of extended and localized states in one-dimensional non-Hermitian Anderson model
• Reentrant localization in a quasiperiodic chain with correlated hopping sequences
• Two-strand ladder network variants: localization, multifractality, and quantum dynamics under an Aubry-André-Harper kind of quasiperiodicity