3D quantum percolation studied by level statistics

We study the metal-insulator transition on a three dimensional quantum percolation model by analyzing energy level statistics. The quantum percolation threshold $\text{pq}$, which is larger than the classical percolation threshold $\text{pc}$, becomes smaller when the time reversal symmetry (TRS) is broken, i.e. $\text{pq}(\mathrm{w}\mathrm{i}\mathrm{t}\mathrm{h}\mathrm{T}\mathrm{R}\mathrm{S})>\text{pq}(\mathrm{w}\mathrm{i}\mathrm{t}\mathrm{h}\mathrm{o}\mathrm{u}\mathrm{t}\mathrm{T}\mathrm{R}\mathrm{S})>\text{pc}$. 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.