Level statistics for quantumk-core percolation

Abstract

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.