Localization Transition on Random Graphs with Chiral and Bogoliubov-de Gennes Symmetry Classes
Disordered Systems and Neural Networks
2025-10-14 v1
Abstract
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.
Keywords
Cite
@article{arxiv.2510.10255,
title = {Localization Transition on Random Graphs with Chiral and Bogoliubov-de Gennes Symmetry Classes},
author = {Daniil Kochergin},
journal= {arXiv preprint arXiv:2510.10255},
year = {2025}
}
Comments
13 pages, 2 figures