Anomalous Random Multipolar Driven Insulators*

We show that in the absence of the time translation symmetry, non-equilibrium topological phases of mattercan exist for an exceptionally long time despite its eventual thermalization. As a prerequisite, we first demon-strate the existence of a long-lived prethermal Anderson localization in 2D with random multipolar driving. Later we show the localization is topologically non-trivial as its bulk orbital magnetization is precisely quantized even though there is no well-defined Floquet eigenergies and states. We further confirm the existence ofthe anomalous random multipolar driven insulators by detecting the quantized charge pumping at the boundries