Transition from quantum chaos to localization in spin chains.

Recent years have seen an increasing interest in quantum chaos and related aspects of spatially extended systems, such as spin chains. However, the results are strongly system dependent: generic approaches suggest the presence of many-body localization, while analytical calculations for certain system classes, here referred to as the "self-dual case," prove adherence to universal (chaotic) spectral behavior. We address these issues studying the level statistics in the vicinity of the latter case, thereby revealing transitions to many-body localization as well as the appearance of several nonstandard random-matrix universality classes.