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.
Cite
@article{arxiv.2408.07355,
title = {Non-Hermitian Quantum Fractals},
author = {Junsong Sun and Chang-An Li and Qingyang Guo and Weixuan Zhang and Shiping Feng and Xiangdong Zhang and Huaiming Guo and Björn Trauzettel},
journal= {arXiv preprint arXiv:2408.07355},
year = {2024}
}
Comments
7 pages, 4 figures