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Many-body localization transition in a periodically driven quantum system isinvestigated using a solution of a matching Bethe lattice problem for Floquetstates of a quantum random energy model with a generalization to more realisticsettings. It turns out that an external periodic field can both suppress andenhance localization depending on field amplitude and frequency which leads tothree distinguishable regimes of field enhanced, controlled and suppresseddelocalization. The results can be verified experimentally in systems of coldatoms and/or interacting spin defects in semiconductors.

Analytical theory of many-body localization in the presence of periodic drive