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arXiv · 2404.11020

Non-Hermitian butterfly spectra in a family of quasiperiodic lattices

Li Wang·Zhenbo Wang·Shu Chen
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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.

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Li Wang, Zhenbo Wang, Shu Chen. 2024-04-17. Non-Hermitian butterfly spectra in a family of quasiperiodic lattices. https://doi.org/10.1103/physrevb.110.l060201

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