Level statistics for quantum $k$-core percolation

TL;DR

This paper investigates the quantum phase transition in $k$-core percolation clusters, revealing a discontinuous metal-insulator transition for $k=3$ and a continuous transition for $k=0$, using level spacing distribution analysis.

Contribution

It provides numerical evidence supporting a new universality class of disorder-driven quantum metal-insulator transitions for $k=3$ on Bethe-like lattices.

Findings

For $k=0$, the quantum critical probability exceeds the geometrical one, indicating a continuous transition.

For $k=3$, the quantum critical probability equals the geometrical one, indicating a discontinuous transition.

Numerical level spacing analysis aligns with previous analytical predictions of a discontinuous MIT for $k=3$.

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 lengthscale for the disorder, $l_d$, is much greater than the coherence length, $l_c$, earlier analytical calculations of quantum conduction on the Bethe lattice demonstrate that for $k=3$ the metal-insulator transition (MIT) is discontinuous, suggesting a new universality class 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 universality class of disorder-driven quantum MITs.