The gapless 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) model with spin SU(2) rotational symmetry. It was recently shown that the spin-S Yao-Lee model has exact deconfined gauge structures for both integer S and half-integer S. Moreover, it was shown that the spin-S Yao-Lee model exhibits Neel spin ordering in the large-S limit. One natural question to ask is whether spin-S Yao-Lee model is a QSOL for S=1. Our large-scale DMRG calculation reveals evidences that the spin-1 Yao-Lee model is a gapless QSOL with no spin ordering.