Synthetic lattices, flat bands and localization in Rydberg quantum simulators.

The most recent manifestation of cold Rydberg atom quantum simulators that employs tailored optical tweezer arrays enables the study of many-body dynamics under so-called facilitation conditions. We show how the facilitation mechanism yields a Hilbert space structure in which the many-body states organize into synthetic lattices, which feature in general one or several flat bands and may support immobile localized states. We focus our discussion on the case of a ladder lattice geometry for which we analyze in particular the influence of disorder generated by the uncertainty of the atomic positions. The localization properties of this system are characterized through two localization lengths which are found to display anomalous scaling behavior at certain energies. Moreover, we discuss the experimental preparation of an immobile localized state, and analyze disorder-induced propagation effects.