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 correlation 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 $\gamma = \ln 2$. We extract two physical length scales $\lambda$ and $\xi$ which constrain the extent of the quantum spin lake $\ell$ from above and below.