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

Ujfalusi, László and Varga, Imre (2014) Quantum percolation transition in 3d: density of states, finite size scaling and multifractality. PHYSICAL REVIEW B, 90 (17). ISSN 2469-9950

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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 Dq and αq , have been determined in the range of 0 ≤ q ≤ 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 ν = 1.622 ± 0.035. However, the mulifractal function, f (α), and the exponents Dq and αq produced anomalous variations along the phase boundary, pQ c (E).

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