Estimate of the critical exponent of the Anderson transition in the three and four dimensional unitary universality classes

Abstract

Disordered non-interacting systems are classified into ten symmetry classes, with the unitary class being the most fundamental. The three and four dimensional unitary universality classes are attracting renewed interest because of their relation to three dimensional Weyl semi-metals and four dimensional topological insulators. Determining the critical exponent of the correlation/localistion length for the Anderson transition in these classes is important both theoretically and experimentally. Using the transfer matrix technique, we report numerical estimations of the critical exponent in a U(1) model in three and four dimensions.

13 pages, 4 figures. Published version. Open access

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• Mobility edge for cold atoms in laser speckle potentials
• Finite-size scaling and multifractality at the Anderson transition for the three Wigner-Dyson symmetry classes in three dimensions
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Cited by in corpus (15)

• Universality classes of the Anderson Transitions Driven by non-Hermitian Disorder
• Unifying the Anderson Transitions in Hermitian and Non-Hermitian Systems
• Transfer matrix study of the Anderson transition in non-Hermitian systems
• Quantum simulation of disordered systems with cold atoms
• Delocalization Transition of Disordered Axion Insulator
• Universality classes of the Anderson transition in three-dimensional symmetry classes AIII, BDI, C, D and CI
• Multifractal finite-size scaling at the Anderson transition in the unitary symmetry class
• Quantum Multicriticality in Disordered Weyl Semimetal
• Anisotropic Topological Anderson Transitions in Chiral Symmetry Classes
• Universality classes of the Anderson transitions driven by quasiperiodic potential in the three-dimensional Wigner-Dyson symmetry classes
• Borel-Padé re-summation of the $\beta$-functions describing Anderson localisation in the Wigner-Dyson symmetry classes
• Localization of Lindbladian Fermions
• Intrinsic (Axion) Statistical Topological Insulator
• Critical behavior of Anderson transitions in higher dimensional Bogoliubov-de Gennes symmetry classes
• Universal Relation between Spectral and Wavefunction Properties at Criticality