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 (20)

• Anderson Transitions
• Localization of ultrasound in a three-dimensional elastic network
• Three-dimensional localization of ultracold atoms in an optical disordered potential
• Statistics and Scaling in Disordered Mesoscopic Electron Systems
• Visualizing Critical Correlations near the Metal-Insulator Transition in Ga1-xMnxAs
• Fractal superconductivity near localization threshold
• Multifractal finite-size-scaling and universality at the Anderson transition
• Exact relations between multifractal exponents at the Anderson transition
• The Anderson transition: time reversal symmetry and universality
• Observation of multifractality in Anderson localization of ultrasound
• Enhancement of superconductivity by Anderson localization
• Multifractality at the quantum Hall transition: Beyond the parabolic paradigm
• Universality and the QCD Anderson Transition
• Wave function statistics at the symplectic 2D Anderson transition: bulk properties
• Anderson transition in the three dimensional symplectic universality class
• Kondo-Anderson Transitions
• Critical Metal Phase at the Anderson Metal-Insulator Transition with Kondo Impurities
• One-parameter Superscaling at the Metal-Insulator Transition in Three Dimensions
• Phase diagram of localization in a magnetic field
• Quantum percolation transition in 3d: density of states, finite size scaling and multifractality

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