Non-Hermitian butterfly spectra in a family of quasiperiodic lattices

Abstract

We propose a family of exactly solvable quasiperiodic lattice models with analytical complex mobility edges, which can incorporate mosaic modulations as a straightforward generalization. By sweeping a potential tuning parameter $\delta$, we demonstrate a kind of interesting butterfly-like spectra in complex energy plane, which depicts energy-dependent extended-localized transitions sharing a common exact non-Hermitian mobility edge. Applying Avila's global theory, we are able to analytically calculate the Lyapunov exponents and determine the mobility edges exactly. For the minimal model without mosaic modulation, a compactly analytic formula for the complex mobility edges is obtained, which, together with analytical estimation of the range of complex energy spectrum, gives the true mobility edge. The non-Hermitian mobility edge in complex energy plane is further verified by numerical calculations of fractal dimension and spatial distribution of wave functions. Tuning parameters of non-Hermitian potentials, we also investigate the variations of the non-Hermitian mobility edges and the corresponding butterfly spectra, which exhibit richness of spectrum structures.

12 pages, 11 figures

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Cited by in corpus (15)

• Asymmetric transfer matrix analysis of Lyapunov exponents in one-dimensional non-reciprocal quasicrystals
• Exact complex mobility edges and flagellate spectra for non-Hermitian quasicrystals with exponential hoppings
• Multifractal-enriched mobility edges and emergent quantum phases in Rydberg atomic arrays
• Scale-free localization versus Anderson localization in unidirectional quasiperiodic lattices
• Localization and mobility edges in non-Hermitian continuous quasiperiodic systems
• 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
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• Anderson-skin dualism: A boundary-dependent effect in non-Hermitian disordered coupled systems
• Exact multiple complex mobility edges and quantum state engineering in coupled 1D quasicystals
• Quantum-to-semiclassical Husimi dynamics of non-Hermitian localization transitions
• Entanglement manifestation of knot topology in a non-Hermitian lattice
• Recent progress on disorder-induced topological phases
• Critical properties in the non-Hermitian Aubry-Andre-Stark model