Predicting topological entanglement entropy in a Rydberg analogue simulator

Predicting the dynamical properties of topological matter is a challenging task, not only in theoretical and experimental settings, but also computationally. Numerical studies are often constrained to studying simplified models and lattices. Here we propose a time-dependent correlated ansatz for the dynamical preparation of a quantum-spin-liquid state on a Rydberg atom simulator. Together with a time-dependent variational Monte Carlo technique, we can faithfully represent the state of the system throughout the entire dynamical preparation protocol. We are able to match not only the physically correct form of the Rydberg atom Hamiltonian but also the relevant lattice topology at system sizes that exceed current experimental capabilities. This approach gives access to global quantities such as the topological entanglement entropy, providing insight into the topological properties of the system. Our results confirm the topological properties of the state during the dynamical preparation protocol, and deepen our understanding of topological entanglement dynamics. We show that, while the simulated state exhibits local properties resembling those of a resonating-valence-bond state, in agreement with experimental observations, it lacks the latter's characteristic topological entanglement entropy signature irrespective of the degree of adiabaticity of the protocol.