Localization Transition on Random Graphs with Chiral and Bogoliubov-de Gennes Symmetry Classes

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.