Winding Numbers and Generalized Mobility Edges in Non-Hermitian Systems

Abstract

The Aubry-André-Harper (AAH) model with a self-dual symmetry plays an important role in studying the Anderson localization. Here we find a self-dual symmetry determining the quantum phase transition between extended and localized states in a non-Hermitian AAH model and show that the eigenenergies of these states are characterized by two types of winding numbers. By constructing and studying a non-Hermitian generalized AAH model, we further generalize the notion of the mobility edge, which separates the localized and extended states in the energy spectrum of disordered systems, to the non-Hermitian case and find that the generalized mobility edge is of a topological nature even in the open boundary geometry in the sense that the energies of localized and extended states exhibit distinct topological structures in the complex energy plane. Finally, we propose an experimental scheme to realize these models with electric circuits.

arXiv comment8 pages including supplementary materials

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• Non-Hermitian Physics
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• Skin effect and winding number in disordered non-Hermitian systems
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• Simulating non-Hermitian quasicrystals with single-photon quantum walks
• Exact mobility edges, $\mathcal{P}\mathcal{T}$-symmetry breaking and skin effect in one-dimensional non-Hermitian quasicrystals
• Phase transitions in a non-Hermitian Aubry-André-Harper model
• Localization and topological transitions in non-Hermitian quasiperiodic lattices
• Topology of anti-parity-time-symmetric non-Hermitian Su-Schrieffer-Heeger model
• Boundary-dependent Self-dualities, Winding Numbers and Asymmetrical Localization in non-Hermitian Quasicrystals
• Non-Hermitian skin effect and self-acceleration
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• Non-Hermitian skin effects on many-body localized and thermal phases
• Non-Hermitian Maryland Model
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• Non-Hermitian pseudo mobility edge in a coupled chain system
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• Exponential size scaling of the Liouvillian gap in boundary-dissipated systems with Anderson localization
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• From scale-free to Anderson localization: a size-dependent transition
• Interplay of nonreciprocity and nonlinearity on mean-field energy and dynamics of a Bose-Einstein condensate in a double-well potential
• Detecting bulk and edge exceptional points in non-Hermitian systems through generalized Petermann factors
• Robust Anderson transition in non-Hermitian photonic quasicrystals
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