Fig. 4: Trimer quantum spin liquid (TQSL) in the PXP model.

A robust TQSL is detected in the PXP model^42,53 with up to third-nearest neighbors blockaded. a Overlap of the ground state with the perfect TQSL state (blue circles) reveals three distinct regions in the 10  ×  6 shape 1 cluster with periodic boundary conditions (see Supplementary Note 3), namely, a trivial phase at small Δ/Ω, a trimer resonatning valence bond (RVB) region with high TQSL fidelity in the middle, and a VBS state with decreasing fidelity at high Δ/Ω. This is further confirmed by considering the fidelity susceptibility [orange squares, evaluated from Eq. (3) with δ = 0.05], wherein two clear peaks stemming from the trivial-TQSL and TQSL-valence bond solid (VBS) transitions appear. b The TQSL fidelity in the spin-liquid region is preserved upon increasing the effective system size, i.e., the number of trimer coverings [equivalent to the maximum independent set (MIS) degeneracy, D_MIS], irrespective of cluster size or aspect ratio. The inset shows the different cluster shapes employed in simulations. The cluster from (a) is emphasized with a green triangle. c The spin-liquid nature of the state with high TQSL overlap is seen by considering the ground-state superposition structure for the typical 6 × 10 shape 3 cluster at Δ/Ω = 3.0, circled in (b). All MIS configurations have dominant almost-equal weights and equal phases (see Supplementary Note 3), while non-MIS configurations have an order-of-magnitude smaller weights.