  Motivated by recent experiments on Ba3NiSb2O9, we investigate possible
quantum spin liquid ground states for spin S=1 Heisenberg models on the
triangular lattice. We use Variational Monte Carlo techniques to calculate the
energies of microscopic spin liquid wave functions where spin is represented by
three flavors of fermionic spinon operators. These energies are compared with
the energies of various competing three-sublattice ordered states. Our approach
shows that the antiferromagnetic Heisenberg model with biquadratic term and
single-ion anisotropy does not have a low-temperature spin liquid phase.
However, for an SU(3)-invariant model with sufficiently strong ring-exchange
terms, we find a paired chiral quantum spin liquid with a Fermi surface of
deconfined spinons that is stable against all types of ordering patterns we
considered. We discuss the physics of this exotic spin liquid state in relation
with the recent experiment and suggest new ways to test this scenario.
