3D quantum percolation studied by level statistics

TL;DR

This paper investigates the quantum phase transition in a 3D quantum percolation model using energy level statistics, revealing the critical threshold's dependence on symmetry and its universality class similarity to Anderson transition.

Contribution

It demonstrates that the quantum percolation threshold is affected by time reversal symmetry and aligns with the universality class of the Anderson transition.

Findings

Quantum percolation threshold exceeds classical threshold

Breaking TRS lowers the quantum percolation threshold

Critical exponents match those of the Anderson transition

Abstract

We study the metal-insulator transition on a three dimensional quantum percolation model by analyzing energy level statistics. The quantum percolation threshold $\pq$, which is larger than the classical percolation threshold $\pc$, becomes smaller when the time reversal symmetry (TRS) is broken, i.e. $\pq({\rm with TRS})>\pq({\rm without TRS})>\pc$. It is shown that critical exponents are consistent with the result of the Anderson transition, suggesting that the quantum percolation problem can be classified into the same universality classes of the Anderson transition. The shape of level statistics at the critical point is also reported.