Predicting Topological Entanglement Entropy in a Rydberg analog simulator

Predicting the dynamical properties of topological matter is a challenging task, not only in theoretical and experimental settings, but also numerically. This work proposes a variational approach based on a time-dependent correlated Ansatz, focusing on the dynamical preparation of a quantum-spin-liquid state on a Rydberg-atom simulator.

Within this framework, we are able to faithfully represent the state of the system throughout the entire dynamical preparation protocol, not only matching the physically correct form of the Rydberg-atom Hamiltonian but also the relevant lattice topology, unlike previous numerical studies. Our approach further gives access to global quantities such as the topological entanglement entropy γ, providing insight into the topological properties of the system.

This is achieved by the introduction of the time-dependent variational Monte Carlo (t-VMC) technique to the dynamics of topologically ordered phases. Upon employing a Jastrow variational Ansatz, we are able to efficiently extend our simulations to system sizes matching state-of-the-art experiments and beyond.

Our results confirm the topological properties of the state during the dynamical preparation protocol, and additionally 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, it lacks the latter's characteristic topological entanglement entropy signature γ = ln(2).