Universal Properties of Many-Body Localization Transitions in Quasiperiodic Systems

The precise nature of many-body localization (MBL) transitions in both random and quasiperiodic (QP) systems remains elusive so far. In particular, whether MBL transitions in QP and random systems belong to the same universality class or two distinct ones has not been decisively resolved. Here, we investigate MBL transitions in one-dimensional (d = 1) QP systems as well as in random systems by state-of-the-art real-space renormalization group (RG) calculation. Our real-space RG shows that MBL transitions in 1D QP systems are characterized by the critical exponent nu approximate to 2.4, which respects the Harris-Luck bound (nu > 1/d) for QP systems. Note that nu approximate to 2.4 for QP systems also satisfies the Harris- Chayes-Chayes-Fisher-Spencer bound (nu > 2/d) for random systems, which implies that MBL transitions in 1D QP systems are stable against weak quenched disorder since randomness is Harris irrelevant at the transition. We shall briefly discuss experimental means to measure nu of QP-induced MBL transitions.