Tunable topological protection in Rydberg lattices via a novel quantum Monte Carlo approach

Rydberg atom arrays have recently been conjectured to host $Z_2$ quantum spin liquids (QSLs) in certain parameter regimes. Due to the strong interactions between these atoms, it is not possible to analytically study these systems, and one must resort to Monte Carlo sampling of the path integral to reach definite conclusions. We use a tailored update, specifically designed to target the low energy excitations of the QSL. This allows us to reliably simulate Rydberg atoms on a triangular lattice in the proposed QSL regime. We identify a correlated paramagnetic phase at low temperatures which hosts topological protection similar to a $Z_2$ spin liquid up to a length scale tuned by Hamiltonian parameters. However, this correlated paramagnet seems to be continuously connected to the trivial paramagnetic regime and thus does not seem to be a true QSL. This result indicates the feasibility of Rydberg atom arrays to act as topological qubits.