Non-Hermitian Quantum Fractals
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arXiv
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| Main Authors: | , , , , , , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866913576250245120 |
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| author | Sun, Junsong Li, Chang-An Guo, Qingyang Zhang, Weixuan Feng, Shiping Zhang, Xiangdong Guo, Huaiming Trauzettel, Björn |
| author_facet | Sun, Junsong Li, Chang-An Guo, Qingyang Zhang, Weixuan Feng, Shiping Zhang, Xiangdong Guo, Huaiming Trauzettel, Björn |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_07355 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Non-Hermitian Quantum Fractals Sun, Junsong Li, Chang-An Guo, Qingyang Zhang, Weixuan Feng, Shiping Zhang, Xiangdong Guo, Huaiming Trauzettel, Björn Mesoscale and Nanoscale Physics 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. |
| title | Non-Hermitian Quantum Fractals |
| topic | Mesoscale and Nanoscale Physics |
| url | https://arxiv.org/abs/2408.07355 |