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 …

We provide a pedagogical review on the calculation of highly excited eigenstates of
disordered interacting quantum systems which can undergo a many-body localization (MBL) …

We report the experimental observation of strong multifractality in wave functions below the
Anderson localization transition in open three-dimensional elastic networks. Our results …

Two exact relations between mutlifractal exponents are shown to hold at the critical point of
the Anderson localization transition. The first relation implies a symmetry of the multifractal …

Multifractals arise in various systems across nature whose scaling behavior is characterized
by a continuous spectrum of multifractal exponents Δ q. In the context of Anderson …

In delocalized systems, particle number fluctuations, also known as quantum surface
roughness, and the mean-square displacement exhibit a temporal power law growth …

We explore the evolution of wave-function statistics on a finite Bethe lattice (Cayley tree)
from the central site (“root”) to the boundary (“leaves”). We show that the eigenfunction …

We present an ultrahigh-precision numerical study of the spectrum of multifractal exponents
Δ q characterizing anomalous scaling of wave function moments⟨| ψ| 2 q⟩ at the quantum …

We generalize universal relations between the multifractal exponent α 0 for the scaling of the
typical wave-function magnitude at a (Anderson) localization-delocalization transition in two …

We study the multifractal analysis (MFA) of electronic wave functions at the localization-
delocalization transition in the three-dimensional Anderson model for very large system …