Dynamical preparation of quantum spin liquids in Rydberg atom arrays

Abstract: We theoretically analyze recent experiments [G. Semeghini et al., Science 374, 1242 (2021)] demonstrating the onset of a topological spin liquid using a programmable quantum simulator based on Rydberg atom arrays. In the experiment, robust signatures of topological order emerge in out-of-equilibrium states that are prepared using a quasi-adiabatic state preparation protocol. We show theoretically that the state preparation protocol can be optimized to target the fixed point of the topological phase -- the resonating valence bond (RVB) state of hard dimers -- in a time that scales linearly with the number of atoms. Moreover, we provide a two-parameter variational manifold of tensor network (TN) states that accurately describe the many-body dynamics of the preparation process. Using this approach we analyze the nature of the non-equilibrium state, establishing the emergence of topological order.