Weak Mott insulators on the triangular lattice: possibility of a gapless nematic quantum spin liquid

We study the energetics of Gutzwiller projected BCS states of various symmetries for the triangular lattice antiferromagnet with a four particle ring exchange using variational Monte Carlo methods. In a range of parameters the energetically favored state is found to be a projected $d_{x^2-y^2}$ paired state which breaks lattice rotational symmetry. We show that the properties of this nematic or orientationally ordered paired spin liquid state as a function of temperature and pressure can account for many of the experiments on organic materials. We also study the ring-exchange model with ferromagnetic Heisenberg exchange and find that amongst the studied ans\"atze, a projected $f-$wave state is the most favorable.