Strong-disorder renormalization group study of the Anderson localization transition in three and higher dimensions

Abstract

We implement an efficient strong-disorder renormalization-group (SDRG) procedure to study disordered tight-binding models in any dimension and on the Erdos-Renyi random graphs, which represent an appropriate infinite dimensional limit. Our SDRG algorithm is based on a judicious elimination of most (irrelevant) new bonds generated under RG. It yields excellent agreement with exact numerical results for universal properties at the critical point without significant increase of computer time, and confirm that, for Anderson localization, the upper critical dimension duc = infinite. We find excellent convergence of the relevant 1/d expansion down to d=2, in contrast to the conventional 2+epsilon expansion, which has little to say about what happens in any d>3. We show that the mysterious mirror symmetry of the conductance scaling function is a genuine strong-coupling effect, as speculated in early work. This opens an efficient avenue to explore the critical properties of Anderson transition in the strong-coupling limit in high dimensions.

Main text: 4 pages, 6 figures Supplemental materials: 4 pages, 7 figures

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• Scale-invariant critical dynamics at eigenstate transitions
• Diffusion in the Anderson model in higher dimensions
• High-Dimensional Disorder-Driven Phenomena in Weyl Semimetals, Semiconductors and Related Systems
• Testing the validity of random-singlet state for long-range hopping models through the scaling of entanglement entropy
• Quantum Griffiths singularity in a three-dimensional superconductor to Anderson critical insulator transition
• Universal Scaling of Electron Transmission for Nearly Ballistic and Quantum Dragon Nanodevices
• Numerical methods for localization
• Critical behavior of Anderson transitions in higher dimensional Bogoliubov-de Gennes symmetry classes