Anderson Transitions
1,437 citations recorded by the source corpus.
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 metalinsulator 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.
Subfields: Atomic and Molecular Physics, and Optics
View Paper: https://www.semanticscholar.org/paper/0382e25d9b2ae4d76dda0af60369f1870a266812
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In Atomic and Molecular Physics, and Optics
Citations in the corpus
- Many-body localization: An introduction and selected topics (2017, neutral): “Note that the simplest example of such a strange phase is the critical state at the Anderson transition point where non-ergodicity can be characterized by a set of multifractal exponents [203].”
- Electronic transport in two-dimensional graphene (2010, background): “Over the past 50 years, there has been much progress towards understanding the physics of Anderson localization (for a recent review, see Evers and Mirlin (2008)).”
- Fractal superconductivity near localization threshold (2010, background): “There is a vast numerical and analytical evidence [78] that the critical wavefunctions at the mobility edge obeys the multifractal statistics.”
- Criterion for Many-Body Localization-Delocalization Phase Transition (2015, neutral): “similar to the distribution of the wave-function tails in the single-particle Anderson insulator [37].”
- Non-Hermitian systems and topology: A transfer-matrix perspective (2018, methodology): “For instance, transfer matrices have been extensively used to study localization in the phenomenological Chalker-Coddington network models [90].”
- Entanglement Phase Transition Induced by the Non-Hermitian Skin Effect (2022, background): “126, 090402 (2021); Transfer matrix study of the Anderson transition in non-Hermitian systems, Phys.”
- Non-Hermitian robust edge states in one dimension: Anomalous localization and eigenspace condensation at exceptional points (2017, background): “A measure of localization of a state ψα is the inverse participation ratio (IPR) [50, 51]:”