Finite-size scaling and multifractality at the Anderson transition for the three Wigner-Dyson symmetry classes in three dimensions

Abstract

The disorder induced metal--insulator transition is investigated in a three-dimensional simple cubic lattice and compared for the presence and absence of time-reversal and spin-rotational symmetry, i.e. in the three conventional symmetry classes. Large scale numerical simulations have been performed on systems with linear sizes up to $L=100$ in order to obtain eigenstates at the band center, $E=0$. The multifractal dimensions, exponents $D_q$ and ${\alpha }_q$, have been determined in the range of $-1\le q\le 2$. The finite-size scaling of the generalized multifractal exponents provide the critical exponents for the different symmetry classes in accordance with values known from the literature based on high precision transfer matrix techniques. The multifractal exponents of the different symmetry classes provide further characterization of the Anderson transition, which was missing from the literature so far.

References in corpus (6)

• Anderson Transitions
• Localization of ultrasound in a three-dimensional elastic network
• Exact relations between multifractal exponents at the Anderson transition
• Multifractality at the quantum Hall transition: Beyond the parabolic paradigm
• Wave function statistics at the symplectic 2D Anderson transition: bulk properties
• Quantum percolation transition in 3d: density of states, finite size scaling and multifractality

Cited by in corpus (7)

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• Deconfinement, chiral transition and localisation in a QCD-like model
• Estimate of the critical exponent of the Anderson transition in the three and four dimensional unitary universality classes
• Borel-Padé re-summation of the $\beta$-functions describing Anderson localisation in the Wigner-Dyson symmetry classes
• Chiral transition, eigenmode localisation and Anderson-like models