Non-Hermitian quantum fractals

作者：Junsong Sun, Chang-An Li, Qingyang Guo, Weixuan Zhang, Shiping Feng, Xiangdong Zhang, Huaiming Guo, Björn Trauzettel · 发表于：Physical review. B./Physical review. B · 年份：2024 · DOI：10.1103/physrevb.110.l201103 · 被引用次数：8 · 研究领域：Advanced Mathematical Theories and Applications、Molecular spectroscopy and chirality、Fractal and DNA sequence analysis

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. 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 another avenue for investigating quantum fractals in non-Hermitian systems.