Quantum k-core conduction on the Bethe lattice

Classical and quantum conduction on a bond-diluted Bethe lattice is considered. The bond dilution is subject to the constraint that every occupied bond must have at least k-1 neighboring occupied bonds, i.e., k -core diluted. In the classical case, we find the onset of conduction for k=2 is continuous while for k=3, the onset of conduction is discontinuous with the geometric random first-order phase transition driving the conduction transition. In the quantum case, treating each occupied bond as a random scatterer, we find for k=3 that the random first-order phase transition in the geometry also drives the onset of quantum conduction giving rise to a new universality class of Anderson localization transitions.