Multifractality and self-averaging at the many-body localization transition

Finite-size effects have been a major and justifiable source of concern for studies of many-body localization, and several works have been dedicated to the subject. In this Letter, however, we discuss yet another crucial problem that has received much less attention, that of the lack of self-averaging and the consequent danger of reducing the number of random realizations as the system size increases. By taking this into account and considering ensembles with a large number of samples for all system sizes analyzed, we find that the generalized dimensions of the eigenstates of the disordered Heisenberg spin-1/2 chain close to the transition point to localization are described remarkably well by an exact analytical expression derived for the noninteracting Fibonacci lattice, thus providing an additional tool for studies of many-body localization.

Automated summary

Finite-size effects and lack of self-averaging are major concerns in studies of many-body localization. By considering a large number of samples for all system sizes, the generalized dimensions of eigenstates can be well described, providing an additional tool for research in this area.