Large disorder and localization

Quenched random disorder is encountered in many types of condensed
matter systems. In quantum systems, the significant role played by
disorder was most dramatically demonstrated in a seminal 1958 paper by
Anderson, which spawned the field of localization that remains an
active industry after over half a century. After the advent of the
Renormalization Group, starting in the 1980s, it was realized that
highly disordered quantum systems could be controllably analyzed using
Strong or Large Disorder Renormalization Group (LDRG) techniques,
especially in one-dimension. Since then, they have been used
profitably in many contexts, including random antiferromagnets, random
fields, phase-coupled oscillators, bosons with strong disorder, and
superconductor-metal transition.

A recent numerical study of the Anderson model of localization at
large disorder revealed that the localized phase rather than being
trivial and uninteresting showed a rather abrupt demarcation between
typical Anderson localized states and resonant states due to atypical
disorder configurations. Unlike many-body models, the single-particle
problem at large disorder can be solved numerically by exact
diagonalization to arbitrary precision and thus serve to check the
accuracy of LDRG methods.  Applying the LDRG technique to the Anderson
model at large disorder, showed a surprise - the standard energy
renormalization technique used for uniform systems is fraught with
difficulties. Instead, a new RG scheme based on eigenstates is found
to work surprisingly well for both density of states and eigenstate
inverse participation ratios throughout the band, and captures the
typical-resonant state boundary very well. This bodes well for the use
of such techniques for electronic models exhibiting many-body
localization.