Variational study of triangular lattice spin-1/2 model with ring exchanges and spin liquid state in kappa-(ET)2Cu2(CN)3

We study triangular lattice spin-1/2 system with antiferromagnetic Heisenberg and ring exchanges using variational approach focusing on possible realization of spin-liquid states. Trial spin liquid wave functions are obtained by Gutzwiller projection of fermionic mean-field states and their energetics is compared against magnetically ordered trial states. We find that in a range of the ring exchange coupling upon destroying the antiferromagnetic order, the best such spin liquid state is essentially a Gutzwiller-projected Fermi sea state. We propose this spin liquid with a spinon Fermi surface as a candidate for the nonmagnetic insulating phase observed in the organic compound kappa-(ET)2Cu2(CN)3, and describe some experimental consequences of this proposal.