Optimizing the Dynamical Preparation of Quantum Spin Lakes on the Ruby Lattice

Quantum spin liquids are elusive long-range entangled states. Motivated by experiments in Rydberg quantum simulators, recent excitement has centered on the possibility of dynamically preparing a state with quantum spin-liquid correlations even when the ground-state phase diagram does not exhibit such a topological phase. Understanding the microscopic nature of such quantum spin "lake" states and their relationship to equilibrium spin-liquid order remains an essential question. Here, we extend the use of approximately symmetric neural quantum states for real-time evolution and directly simulate the dynamical preparation in systems of up to N=384 atoms. We analyze a variety of spin-liquid diagnostics as a function of the preparation protocol and optimize the extent of the quantum spin lake thus obtained. In the optimal case, the prepared state shows spin-liquid properties extending over half the system size, with a topological entanglement entropy plateauing close to γ=ln2. We extract two physical length scales, λ_{e} and ξ_{m}, which constrain the extent of the quantum spin lake ℓ from above and below.