Mean-Field Parton Description of a Rydberg Quantum Spin Liquid from Microscopic Properties*

Quantum Spin Liquids (QSL) represent an exotic phase of matter elusive to experiments. One hallmark property is the absence of magnetic spin order even at zero temperature. Despite numerous attempts, the unambiguous experimental confirmation of QSL states remains difficult. In this context, the possibility of realizing QSL physics on Rydberg atom-based quantum simulators has been a promising avenue for investigation [Semeghini et al., Science 374 (2021)].

Recently, the existence of a QSL state has been investigated numerically with Exact Diagonalization (ED) in a system of Rydberg atoms on a honeycomb lattice featuring density-dependent Peierls phases [Ohler et al., PRR 5 (2023)]. Later investigations using projective symmetry group arguments [Tarabunga et al. PRB 108 (2023)] confirmed the state to be a chiral spin liquid by comparing ground-states of ansatz Hamiltonians with ED results.

In this work, we take a different approach, deriving explicitly the mean-field parton Hamiltonian starting from the microscopic Rydberg properties. We then determine the mean-field ground-state self-consistently, which yields a more accurate representation of the Rydberg ground-state. It shows large overlap with the ED simulation but is in principle not restricted to small system sizes.