Analysis of many-body localization from different perspectives

Finite-size effects have been a major and justifiable source of concern in the analysis of many-body localization. Another crucial problem, that is sometimes overlooked, is the lack of self-averaging and the consequent danger of reducing the number of random realizations as the system size increases. In our work, we take into account the issue of self-averaging and investigate how different quantities, that are used to determine the possible transition from an ergodic to a many-body localized phase, depend on system size. Our analysis focuses on the one-dimensional spin-1/2 Heisenberg model with onsite disorder. We find that level statistics, structure of the eigenstates, and dynamics may lead to contradictory results. For a fixed disorder strength, one quantity may indicate chaos enhancement as the system size increases, while another one may suggest approach to a localized phase.