Quantum percolation transition in 3d: density of states, finite size scaling and multifractality

TL;DR

This study investigates the quantum percolation transition in three dimensions, analyzing eigenstates' multifractality and confirming its universality class with the Anderson model, using large-scale numerical simulations.

Contribution

It provides a detailed numerical analysis of the 3D quantum percolation transition, including multifractal analysis and critical exponents, establishing its universality class.

Findings

Critical exponent of localization length: ν=1.622±0.035

Multifractal function f(α) appears universal

Exponents D_q and α_q show anomalous variations along the phase boundary

Abstract

The phase diagram of the metal-insulator transition in a three dimensional quantum percolation problem is investigated numerically based on the multifractal analysis of the eigenstates. The large scale numerical simulation has been performed on systems with linear sizes up to $L=140$. The multifractal dimensions, exponents $D_q$ and $\alpha_q$, have been determined in the range of $0\leq q\leq 1$. Our results confirm that this problem belongs to the same universality class as the three dimensional Anderson model, the critical exponent of the localization length was found to be $\nu=1.622\pm 0.035$. The mulifractal function, $f(\alpha)$, appears to be universal, however, the exponents $D_q$ and $\alpha_q$ produced anomalous variations along the phase boundary, $p_c^Q(E)$.