Variational Monte Carlo study of quantum spin=1 liquid phases in the extended triangular-lattice Heisenberg model

Recent experiments in the compound Ba3NiSb2O9 [PRL 107, 197204] indicated that quantum-spin liquid phases in a spin S=1 anti-ferromagnet may exist. Motivated by these experiments, we construct quantum spin=1 liquid states with three flavors of fermionic spinons. We use variational Monte Carlo calculations to investigate the phase diagram of a triangular-lattice quantum Heisenberg model with single-ion anisotropy, bi-quadratic, and ring-exchange terms. We compare the energies of the spin-liquid states with conventional magnetically ordered states. We find that in some parameter ranges, an exotic gapless U(1) spin liquid is stabilized. In other parameter ranges, a BCS pairing instability with unconventional symmetry gaps out some of the spinons. We discuss our findings in relation with present and future experiments.