Universal properties of many-body localization criticality in 1D quasiperiodic systems

The nature of many-body localization (MBL) transitions in 1D quasi-periodic systems remains illusive so far. We employ real-space renormalization group (RG) to investigate universal properties of such MBL transitions. By performing the state-of-the-art real-space RG analysis to systems with large size, our results show that the MBL transitions in 1D quasiperiodic systems have the critical exponent $\nu>2$ that exceeds the Harris-CCFS bound. Consequently, the MBL transitions in quasi-periodic 1D systems are stable against weak quenched random disorder. We also discuss several interesting features related to quasiperiodic-driven MBL systems.