Ring Structure in the Complex Plane: A Fingerprint of non-Hermitian Mobility Edge

Abstract

By Avila's global theory, we analytically reveal that the non-Hermitian mobility edge will take on a ring structure in the complex plane, which we name as "mobility ring". The universality of mobility ring has been checked and supported by the Hermitian limit, $PT$-symmetry protection and without $PT$-symmetry cases. Further, we study the evolution of mobility ring versus quasiperiodic strength, and find that in the non-Hermitian system, there will appear multiple mobility ring structures. With cross-reference to the multiple mobility edges in Hermitian case, we give the expression of the maximum number of mobility rings. Finally, by comparing the results of Avila's global theorem and self-duality method, we show that self-duality relation has its own limitations in calculating the critical point in non-Hermitian systems. As we know, the general non-Hermitian system has a complex spectrum, which determines that the non-Hermitian mobility edge can but exhibit a ring structure in the complex plane.

4.5+4 pages,4+2 figures

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• Non-Hermitian butterfly spectra in a family of quasiperiodic lattices
• Asymmetric transfer matrix analysis of Lyapunov exponents in one-dimensional non-reciprocal quasicrystals
• Identifying non-Hermitian critical points with quantum metric
• Exact complex mobility edges and flagellate spectra for non-Hermitian quasicrystals with exponential hoppings
• Measurement-Induced Entanglement Phase Transition in Free Fermion Systems
• Fate of non-Hermitian free fermions with Wannier-Stark ladder
• Scale-free localization versus Anderson localization in unidirectional quasiperiodic lattices
• Quasiperiodicity-induced bulk localization with self similarity in non-Hermitian systems
• Emergent multi-loop nested point gap in a non-Hermitian quasiperiodic lattice
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• Reentrant localization transition induced by a composite potential
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• Antichiral and trap-skin dynamics in a nonreciprocal bosonic two-leg ladder with artificial magnetic flux
• Exact mobility line and mobility ring in the complex energy plane of a flat band lattice with a non-Hermitian quasiperiodic potential
• Mobility rings in a non-Hermitian non-Abelian quasiperiodic lattice
• The global phase diagram of the cluster-XY spin chain with dissipation
• Exact multiple complex mobility edges and quantum state engineering in coupled 1D quasicystals
• Vacuum induced three-body delocalization in cavity quantum materials
• Family of self-dual quasicrystals with critical Phases
• Critical properties in the non-Hermitian Aubry-Andre-Stark model
• Recent progress on disorder-induced topological phases
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• Quasiperiodic Skin Criticality in an Exactly Solvable Non-Hermitian Quasicrystal