Non-Hermitian Quantum Fractals

Abstract

The first quantum fractal discovered in physics is the Hofstadter butterfly. It stems from large external magnetic fields. We discover instead a new class of non-Hermitian quantum fractals (NHQFs) emerging in coupled Hatano-Nelson models on a tree lattice in absence of any fields. Based on analytic solutions, we are able to rigorously identify the self-similar recursive structures in energy spectrum and wave functions. We prove that the complex spectrum of NHQFs bears a resemblance to the Mandelbrot set in fractal theory. The self-similarity of NHQFs is rooted in the interplay between the iterative lattice configuration and non-Hermiticity. Moreover, we show that NHQFs exist in generalized non-Hermitian systems with iterative lattice structures. Our findings open a new avenue for investigating quantum fractals in non-Hermitian systems.

7 pages, 4 figures

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Cited by in corpus (6)

• Quasiperiodicity-induced bulk localization with self similarity in non-Hermitian systems
• Non-Hermitian Skin Effect Along Hyperbolic Geodesics
• Inner non-Hermitian skin effect on Bethe lattice
• Multifractal statistics of non-Hermitian skin effect on the Cayley tree
• Mobility-edge-embedded Hofstadter butterfly from a tilt-induced quasiperiodic potential
• Topological states and flat bands in exactly solvable decorated Cayley trees