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.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.

arXiv:1203.4599Physical Review BAug 24, 20121 citation

Quantum correlated percolation

Liang Cao, M. Jeng, Jennifer M. Schwarz

Bulletin of the American Physical SocietyMar 18, 20090 citations

Percolation methods for disordered quantum Ising models

Charles M. Newman, Michael Aizenman, Abel Klein

Jan 1, 199334 citations

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.