Localization Transition on Random Graphs with Chiral and Bogoliubov-de Gennes Symmetry Classes
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arXiv
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866918158754906112 |
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| author | Kochergin, Daniil |
| author_facet | Kochergin, Daniil |
| contents | We studied single-particle Anderson localization in ensembles of graphs that correspond to chiral and Bogoliubov-de Gennes (BdG) symmetry classes. For a random biregular bipartite graph with chiral symmetry, the density of states was found using the cavity approach. Calculating the fractal dimension shows the effects of disordered zero modes. For Bogoliubov-de Gennes ensembles with an underlying random regular graph (RRG), the density of states was calculated both numerically and analytically. The ensembles BdG-RRG with symmetry-conserving diagonal disorder in the delocalized phase have a smaller fractal dimension compared to the usual RRG. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_10255 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Localization Transition on Random Graphs with Chiral and Bogoliubov-de Gennes Symmetry Classes Kochergin, Daniil Disordered Systems and Neural Networks We studied single-particle Anderson localization in ensembles of graphs that correspond to chiral and Bogoliubov-de Gennes (BdG) symmetry classes. For a random biregular bipartite graph with chiral symmetry, the density of states was found using the cavity approach. Calculating the fractal dimension shows the effects of disordered zero modes. For Bogoliubov-de Gennes ensembles with an underlying random regular graph (RRG), the density of states was calculated both numerically and analytically. The ensembles BdG-RRG with symmetry-conserving diagonal disorder in the delocalized phase have a smaller fractal dimension compared to the usual RRG. |
| title | Localization Transition on Random Graphs with Chiral and Bogoliubov-de Gennes Symmetry Classes |
| topic | Disordered Systems and Neural Networks |
| url | https://arxiv.org/abs/2510.10255 |