Multifractal statistics of non-Hermitian skin effect on the Cayley tree
Fuente:
arXiv
Guardado en:
| Autores principales: | , , , , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2024
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866929732603346944 |
|---|---|
| author | Hamanaka, Shu Iliasov, Askar A. Neupert, Titus Bzdušek, Tomáš Yoshida, Tsuneya |
| author_facet | Hamanaka, Shu Iliasov, Askar A. Neupert, Titus Bzdušek, Tomáš Yoshida, Tsuneya |
| contents | Multifractal analysis is a powerful tool for characterizing the localization properties of wave functions. Despite its utility, this tool has been predominantly applied to disordered Hermitian systems. Multifractal statistics associated with the non-Hermitian skin effect remain largely unexplored. Here, we demonstrate that the tree geometry induces multifractal statistics for the single-particle skin states on the Cayley tree by deriving the analytical expression of multifractal dimensions. This sharply contrasts with the absence of multifractal properties for conventional single-particle skin effects in crystalline lattices. Our work uncovers the unique feature of the skin effect on the Cayley tree and provides a novel mechanism for inducing multifractality in open quantum systems without disorder. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_11024 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Multifractal statistics of non-Hermitian skin effect on the Cayley tree Hamanaka, Shu Iliasov, Askar A. Neupert, Titus Bzdušek, Tomáš Yoshida, Tsuneya Mesoscale and Nanoscale Physics Statistical Mechanics Quantum Physics Multifractal analysis is a powerful tool for characterizing the localization properties of wave functions. Despite its utility, this tool has been predominantly applied to disordered Hermitian systems. Multifractal statistics associated with the non-Hermitian skin effect remain largely unexplored. Here, we demonstrate that the tree geometry induces multifractal statistics for the single-particle skin states on the Cayley tree by deriving the analytical expression of multifractal dimensions. This sharply contrasts with the absence of multifractal properties for conventional single-particle skin effects in crystalline lattices. Our work uncovers the unique feature of the skin effect on the Cayley tree and provides a novel mechanism for inducing multifractality in open quantum systems without disorder. |
| title | Multifractal statistics of non-Hermitian skin effect on the Cayley tree |
| topic | Mesoscale and Nanoscale Physics Statistical Mechanics Quantum Physics |
| url | https://arxiv.org/abs/2408.11024 |