Breakdown of the correspondence between the real-complex and delocalization-localization transitions in non-Hermitian quasicrystals

Abstract

The correspondence between the real-complex transition in energy and delocalization-localization transition is well-established in a class of Aubry-Andr'e-Harper model with exponential non-Hermitian on-site potentials. In this paper, we study a generalized Aubry-Andr'e model with off-diagonal modulation and non-Hermitian on-site potential. We find that, when there exists an incommensurate off-diagonal modulation, the correspondence breaks down, although the extended phase is maintained in a wide parameter range of the strengths of the on-site potential and the off-diagonal hoppings. An additional intermediate phase with a non-Hermitian mobility edge emerges when the off-diagonal hoppings become commensurate. This phase is characterized by the real and complex sections of the energy spectrum corresponding to the extended and localized states. In this case, the aforementioned correspondence reappears due to the recovery of the PT-symmetry.

arXiv comment9 pages, 10 figures

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• 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
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• Power law hopping of single particles in one-dimensional non-Hermitian quasicrystals
• 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
• Long-range hopping in a quasiperiodic potential weakens the non-Hermitian skin effect
• Scale-free localization versus Anderson localization in unidirectional quasiperiodic lattices
• Non-equilibrium dynamics of localization phase transition in the non-Hermitian Disorder-Aubry-André model
• Exact mobility line and mobility ring in the complex energy plane of a flat band lattice with a non-Hermitian quasiperiodic potential
• Exact multiple complex mobility edges and quantum state engineering in coupled 1D quasicystals
• Coexistence of topological Anderson insulator and multifractal critical phase in a non-Hermitian quasicrystal