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Although quantum spin liquids are elusive, they are a canonical example of strongly correlated quantum states characterized by long-range quantum entanglement. Recently, direct characterization of a gapped topological $\mathbb{Z}_2$ spin liquid was observed in a system of Rydberg atoms arranged on a ruby ​​lattice. Here we describe a concrete realization of a radically different class of spin liquids in a honeycomb arrangement of Rydberg atoms. Investigating the quantum state diagram of this system, using both density-matrix renormalization group and exact diagonalization simulations, characterizes several density-wave array phases and explains their origins. More interestingly, in the region where the third neighboring atom is within the Rydberg blockade radius, a new ground state is found — $\mathrm{U}(1)\times \mathrm{U}(1)$ local Symmetry — formed from the superposition of classical {\it trimer} constructs on a double triangular lattice. The fidelity of this trimer spin liquid state can be enhanced by dynamic preparation. This is explained by the Rydberg blockade-based projection mechanism associated with the smooth turn-off of the laser drive. Finally, we discuss the robustness of the trimer spin-liquid phase under realistic experimental parameters and show that the proposal can be readily implemented in current Rydberg atomic quantum simulators.

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