Interplay of quasi-periodic potential and disorder in 3D Anderson model

Both random disorder and quasi-periodic potential can localize quantum mechanical wave functions. We investigate how the two factors interplay in the localization phenomenon by studying 3D Anderson model in the presence of an anisotropic quasi-periodic potential along z direction. We study the model numerically with the transfer matrix method and obtain a qualitative phase diagram. We observe that, at certain strength of the quasi-periodic potential, the model displays a two-stage phase transition as the disorder strength increases: it is localized at small disorder strength, then becomes delocalized, and eventually enters the localized phase again. Our result implies that quasiperiodic potential and disorder compete with each other in localizing wave functions in an appropriate parameter regime.