  In this paper, we explore the relationship between strong spin-orbit coupling
and spin liquid physics. We study a very general model on the triangular
lattice where spin-orbit coupling leads to the presence of highly anisotropic
interactions. We use variational Monte Carlo to study both $U(1)$ quantum spin
liquid states and ordered ones, via the Gutzwiller projected fermion
construction. We thereby obtain the ground state phase diagram in this phase
space. We furthermore consider effects beyond the Gutzwiller wavefunctions for
the spinon Fermi surface quantum spin liquid, which are of particular
importance when spin-orbit coupling is present.
