Anderson Transitions

TL;DR

This paper reviews the physics of Anderson transitions, covering metal-insulator and quantum Hall transitions, emphasizing recent advances in multifractality, symmetry classification, and critical theories through analytical and numerical methods.

Contribution

It provides a comprehensive overview of recent developments in understanding Anderson transitions, including multifractality, symmetry classes, and critical models in disordered systems.

Findings

Multifractality of critical wave functions analyzed.

Symmetry classification of disordered systems discussed.

Numerical simulations support theoretical models.

Abstract

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.