Regensburg 2025 – wissenschaftliches Programm
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TT: Fachverband Tiefe Temperaturen
TT 53: Topology: Other Topics
TT 53.7: Vortrag
Freitag, 21. März 2025, 11:15–11:30, H32
Non-Hermitian Quantum Fractals and Inner Non-Hermitian Skin Effects — Changan Li1, Junsong Sun2, Huaming Guo2, and •Björn Trauzettel1 — 1Institute for Theoretical Physics and Astrophysics, University of Würzburg, 97074 Würzburg, Germany — 2School of Physics, Beihang University, Beijing, 100191, China
The first quantum fractal discovered in physics is the Hofstadter butterfly. It stems from large external magnetic fields. We discover instead a class of non-Hermitian quantum fractals (NHQFs) emerging in coupled Hatano-Nelson models on a tree lattice in the absence of any fields. Based on analytic solutions, we are able to rigorously identify the self-similar recursive structures in the energy spectrum and wave functions. We prove that the complex spectrum of NHQFs bears a resemblance to the Mandelbrot set in fractal theory. We further investigate the non-Hermitian Su-Schrieffer-Heeger (SSH) model on Bethe lattice, revealing a novel localization phenomenon coined inner non-Hermitian skin effect. Our findings open another avenue for investigating quantum fractals in non-Hermitian systems.
Keywords: quantum fractals; non-Hermitian physics; Hatano-Nelson model; Su-Schrieffer-Heeger model; non-Hermitian skin effects