Multiple scar towers in Rydberg quantum simulators

Analog quantum simulators have led to significant insight into the non-equilibrium behavior of many-body systems. Programmable Rydberg simulators, in particular, have uncovered the existence of quantum many-body scar states. The conventional understanding of these scar states is that they are a small subset of non-ergodic eigenstates embedded in a thermal spectrum. However, recent work has shown that the prototypical PXP model has more scars than those first probed experimentally. In this talk, we will discuss the impact of these additional sets of scars on the dynamics of Rydberg simulators. We will show that the magnetization and temporal correlators exhibit oscillations for almost any initial product state with a frequency close to that of the conventional set of scars. We will argue that these oscillations arise due to the presence of multiple sets of scars that satisfy an approximate su(2) algebra. Finally, we will discuss strategies to detect the presence of these additional sets of scar states in digital quantum simulators using quantum typicality.