Gapped Quantum Spin-Orbital Liquid in the Spin-1 Yao-Lee Model

The spin-1/2 Yao-Lee model is an exactly solvable quantum spin-orbital liquid (QSOL) with full SU(2) spin rotational symmetry. Recent theoretical work has shown that its spin-S generalization possesses exact deconfined gauge structures for both integer and half-integer S, and exhibits Néel order in the large-S limit. An important open question is whether the spin-1 Yao-Lee model preserves the liquid character or develops magnetic order. Using large-scale density matrix renormalization group (DMRG) simulations, we find compelling evidence that the spin-1 Yao-Lee model realizes a gapped quantum spin-orbital liquid with no long-range spin order. These findings demonstrate that strong quantum fluctuations persist at integer spin S = 1, suggesting that orbital dynamics may stabilize the QSOL phase.