Mitchell Institute for Fundamental Physics & Astronomy
College Station, Texas 77843
We study the problem of single particle Anderson Localization on the Random Regular Graph (RRG) via exact diagonalization. Interest to this problem has recently revived largely in connection with the Many-Body Localization (MBL). MBL can be thought of as localization in the Fock space of Slater determinants, which play the role of lattice sites in a disordered tight binding model. In contrast to a d-dimensional lattice, the structure of Fock space is hierarchical and thus resembles a RRG. We study this problem numerically and show that contrary to recent claims, if shows regular localization transition with peculiar finite-size effects which obscure the existence of a sharp transition up to very large graph sizes.