Fig. 1: Trimer quantum spin liquid (TQSL) on a honeycomb lattice of Rydberg atoms.

a In the regime where three nearest-neighbor Rydberg atoms are within the blockade radius (k = 3 shell, shown in orange), the blockade-obeying configurations map exactly to the trimer coverings of the triangular lattice with vertices at the centers of the hexagons³¹. The number of trimer coverings on the triangular lattice grows exponentially with the system size³⁷. b The TQSL is an equal superposition of exponentially many trimer coverings (one covering shown with filled triangles), and is characterized by a U(1) × U(1) local symmetry due to the tripartite nature of triangular lattice with respect to trimers³⁹. For the tripartition and the trimer configuration shown, we assign two sets of electric fields directed from A to B and from B to C sublattices (arrows). The two U(1) degrees of freedom can be related to two conservation laws, as the independent fluxes are equal to the charges N_A − N_B and N_B − N_C enclosed by a closed loop. c Quantum phase diagram of Rydberg atoms on a 32 × 4 honeycomb lattice retaining three strongest interactions, as obtained by density matrix renormalization group (DMRG)⁴⁶. The boundaries of the three ordered phases (Néel, columnar, and brick) are mapped out by entanglement entropy, energy susceptibility, and fidelity susceptibility peaks (full lines). In addition, a region with a large entanglement entropy is distinguished by fidelity and energy susceptibility (dashed lines) measurements in the regime where third-nearest neighbors are blockaded. The properties of this unordered phase agree with the expected properties of the TQSL state on a finite cylinder.