Ultraslow Growth of Number Entropy in an l-Bit Model of Many-Body Localization

We demonstrate that slow growth of the number entropy following a quench from a local product state is consistent with many-body localization. To do this, we construct a novel random circuit l -bit model with exponentially localized l-bits and exponentially decaying interactions between them. We observe an ultraslow growth of the number entropy starting from a Neel state, saturating at a value that grows with system size. This suggests that the observation of such growth in microscopic models is not sufficient to rule out many-body localization.