Universality class of many-body localization transition on 1D system with both random and quasiperiodic potentials

Whether MBL transitions in quasiperiodic (QP) and random systems belong to the same universality class or two distinct ones has not been decisively resolved so far. 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 $\nu\approx 2.4$, which respects the Harris-Luck bound ($\nu>1/d$) for QP systems. Note that $\nu\approx 2.4$ for QP systems also satisfies the Harris-CCFS 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. By investigating the system with both QP and random potentials via real-space RG, we directly show that the QP-induced MBL criticality is robust against small randomness. Consequently, our real-space RG results imply that there are indeed two stable universality classes of MBL criticalities. We further discuss the possible scenario of the global phase diagram with both types of MBL transitions.

[1] Shi-Xin Zhang and Hong Yao, arXiv:1805.05958 (to appear in Phys. Rev. Lett.)