Optimizing randomized potentials for inhibiting thermalization in one-dimensional systems

There is a growing interest in applying different external potentials other than the conventional uniform disorder for inhibiting thermalization and realizing the many-body localization (MBL) phase. Various types of external potentials have been explored, e.g., linear/quasiperiodic potentials and discrete disorder, but what type of potentials is the most "effective" for inducing MBL remains elusive. In this work, we formally introduce the problem of the optimal randomized potential from two aspects, which is to find the optimal on-site energy distribution so that (1) the required random field strength for the onset of MBL (i.e., W in the literature) is the minimal, and (2) the thermalization occurs the slowest after the system is prepared in an out-of-equilibrium state. We choose the spinless fermionic chain to study the problem using two complementary methods. For short chains (L < 20), we employ exact numerical approaches for (1) diagnosing MBL transitions and (2) simulating the dynamics of the entanglement entropy. For longer chains [L similar to O(100)], we employ a modified real-space renormalization group (RSRG) approach to trade off accuracy for simulation sizes and scaling properties. Both methods predict that random potentials with a certain degree of polarization towards binary disorder will favor the MBL more than the uniform distribution. For some studied cases, the optimal random distribution lies in between the uniform and binary disorder. We attribute that to the competition between increased on-site energy fluctuation and enhanced degeneracy near the distribution edge (+/- W). While precisely determining the functional form of the optimal random distribution is not feasible at present, our results could be useful for engineering more efficient potentials for realizing MBL in mesoscopic systems.