Predicting Topological Entanglement Entropy in a Rydberg analog simulator

TL;DR

This paper introduces a variational Monte Carlo approach to simulate and analyze the dynamical creation of topological quantum states in Rydberg-atom systems, providing insights into topological entanglement during state preparation.

Contribution

The work develops a scalable, flexible variational method that accurately models topological state dynamics in Rydberg simulators, surpassing previous simplified numerical models.

Findings

Confirmed topological order during state preparation

State exhibits RVB-like properties without the expected topological entanglement entropy signature

Method matches experimental observations and extends to large system sizes

Abstract

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. The flexibility of our approach does not only allow one to match the physically correct form of the Rydberg-atom Hamiltonian but also the relevant lattice topology. This is unlike previous numerical studies which were constrained to simplified versions of the problem through the modification of both the Hamiltonian and the lattice. Our approach further gives access to global quantities such as the topological entanglement entropy ($\gamma$), 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 with a scalable number of parameters, we are able to efficiently extend our simulations to system sizes matching state-of-the-art experiments and beyond. Our results corroborate experimental observations, confirming the presence of topological order during the dynamical state-preparation protocol, and additionally deepen our understanding of topological entanglement dynamics. We show that, while the simulated state exhibits (global) topological order and local properties resembling those of a resonating-valence-bond (RVB) state, it lacks the latter's characteristic topological entanglement entropy signature $\gamma = \ln(2)$, irrespective of the degree of adiabaticity of the protocol.