Level statistics for quantum k-core percolation

Quantum k-core percolation is the study of quantum transport on k-core percolation clusters where each occupied bond must have at least k occupied neighboring bonds. As the bond occupation probability p is increased from zero to unity, the system undergoes a transition from an insulating phase to a metallic phase. When the length scale for the disorder l _d is much greater than the coherence length l _c, earlier analytical calculations of quantum conduction on the Bethe lattice demonstrated that for k=3 the metal-insulator transition (MIT) is discontinuous, suggesting a new type of disorder-driven quantum MITs. Here, we numerically compute the level spacing distribution as a function of bond occupation probability p and system size on a Bethe-like lattice. The level spacing analysis suggests that for k=0, p _q, the quantum percolation critical probability, is greater than p _c, the geometrical percolation critical probability, and the transition is continuous. In contrast, for k=3, p _q=p _c, and the transition is discontinuous such that these numerical findings are consistent with our previous work to reiterate a new random first-order phase transition and therefore a new universality class of disorder-driven quantum MITs.