How is multifractality broken in a perturbed quantum system?

Multifractal analysis has been shown to be powerful in order to describe critical wave field in physics. Criticality here means that the system is exactly at the transition point (in parameter space) between two very distinct states (e.g. liquid/gas or metal/insulator). For the metal/insulator transition, Anderson model admits eigenstates, which are multifractal in the infinitely large system size limit. It has also been numerically observed that a precise 1d kicked quantum map can have multifractal eigenstates in the semiclassical regime. In this talk I will review how multifractality is observed in these systems and how it is changed when the systems are slightly perturbed.