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

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 $0\le q\le 1$. 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, $p_c^Q(E)$.

arXiv comment15 pages, 10 figures with altogether 37 subparts

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• Drawing Phase Diagrams of Random Quantum Systems by Deep Learning the Wave Functions
• Finite-size scaling and multifractality at the Anderson transition for the three Wigner-Dyson symmetry classes in three dimensions
• Anderson transition and multifractals in the spectrum of the Dirac operator of Quantum Chromodynamics at high temperature
• Phase Diagrams of Three-Dimensional Anderson and Quantum Percolation Models using Deep Three-Dimensional Convolutional Neural Network
• Multifractal finite-size scaling at the Anderson transition in the unitary symmetry class
• Quantum percolation on Lieb Lattices
• Analysis of Kohn-Sham Eigenfunctions Using a Convolutional Neural Network in Simulations of the Metal-insulator Transition in Doped Semiconductors