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.

arXiv comment13 pages, 4 figures. Published version. Open access

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• Critical Exponent of the Anderson Transition using Massively Parallel Supercomputing
• 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
• High-Dimensional Disorder-Driven Phenomena in Weyl Semimetals, Semiconductors and Related Systems
• 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