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      Multifractal finite-size scaling at the Anderson transition in the unitary symmetry class

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          Abstract

          We use multifractal finite-size scaling to perform a high-precision numerical study of the critical properties of the Anderson localization-delocalization transition in the unitary symmetry class, considering the Anderson model including a random magnetic flux. We demonstrate the scale invariance of the distribution of wavefunction intensities at the critical point and study its behavior across the transition. Our analysis, involving more than \(4\times10^6\) independently generated wavefunctions of system sizes up to \(L^3=150^3\), yields accurate estimates for the critical exponent of the localization length, \(\nu=1.446 (1.440,1.452)\), the critical value of the disorder strength and the multifractal exponents.

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          Most cited references 38

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          Scaling Theory of Localization: Absence of Quantum Diffusion in Two Dimensions

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            Disordered electronic systems

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              Anderson Transitions

               F Evers,  A Mirlin (2007)
              The physics of Anderson transitions between localized and metallic phases in disordered systems is reviewed. The term ``Anderson transition'' is understood in a broad sense, including both metal-insulator transitions and quantum-Hall-type transitions between phases with localized states. The emphasis is put on recent developments, which include: multifractality of critical wave functions, criticality in the power-law random banded matrix model, symmetry classification of disordered electronic systems, mechanisms of criticality in quasi-one-dimensional and two-dimensional systems and survey of corresponding critical theories, network models, and random Dirac Hamiltonians. Analytical approaches are complemented by advanced numerical simulations.
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                Author and article information

                Journal
                17 July 2017
                Article
                1707.05701

                http://arxiv.org/licenses/nonexclusive-distrib/1.0/

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                11 pages, 8 figures. arXiv admin note: text overlap with arXiv:1107.5736
                cond-mat.dis-nn

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