Localization in two-dimensional many-body quasiperiodic models

Many-body localization (MBL) provides a mechanism to avoid thermalization in interacting systems. It is well understood that the MBL phase can exist in closed one-dimensional systems subjected to random disorder, quasiperiodic modulations, or homogeneous electric fields. However, the fate of MBL in higher dimensions remains unclear. Although some experiments on randomly disordered two-dimensional (2D) systems observe a stable MBL phase on intermediate time scales, recent theoretical works show that the phenomenon cannot persist forever and in a thermodynamic limit due to the rare regions and the avalanche instability. On the other hand, quasiperiodic systems do not host rare regions, and the avalanche instability is avoided; yet, the existence of an MBL phase in these systems remains to date largely unexplored. Using the numerical method of time-dependent variational principle, we investigate the localization properties of the many-body 2D Aubry-Andre´ quasiperiodic model by studying its out-of-equilibrium dynamics. We show that a stable MBL phase exists in the thermodynamic limit, in contrast to random disorder. Furthermore, we show that deterministic lines of weak potential, which appear in this model, support transport while keeping the localized parts of the system unchanged.