Is the Rydberg ruby-lattice spin liquid an equilibrium ground state?
In plain words
A 2021 experiment saw signs of a quantum spin liquid, a state with hidden long-range quantum entanglement, in atoms on a ruby-shaped lattice. It is unclear whether this was a true lowest-energy state or a product of fast driving.
Precise statement
$H = \sum_i (\Omega/2) X_i - \Delta n_i + \sum_{ij} V_{ij} n_i n_j$ with $V_{ij} = C_6/r_{ij}^6$ on the ruby lattice. Determine whether the ground state at some $(\Delta/\Omega, R_b/a)$ has $Z2$ topological order, diagnosed by topological entanglement entropy $\gamma = \ln 2$ or anyon braiding, with the full $1/r^6$ tails kept. Answer: yes or no with the parameter window.
What would settle it
Large-cylinder DMRG or tensor-network calculations with the full interaction showing $\gamma = \ln 2$, matched by an adiabatic preparation that measures anyon statistics.
Status in the literature
Unverified note
Quantum Monte Carlo finds a renormalized classical spin liquid at $T/\Omega = 0.01 \text{ to } 0.5$ in the ruby PXP model, with a shifted entropy plateau once van der Waals tails are kept (Wang and Pollet, arXiv:2406.07110); optimized ramps reach spin-liquid correlations over half the system (Vu et al., PRL 2026, arXiv:2512.09040); ground-state topological order with full $1/r^{6}$ tails is unconfirmed.