Phase Diagram of the 2D Fermionic Ring Exchange Only Model

There has been significant interest in understanding non-Fermi liquid phases. Recently, DMRG studies on 2-leg ladders have suggested the presence of such a phase (the $d$-wave metal) in the $t-J-K$ model on a 2D square lattice, where $K$ is a nearest neighbor ring exchange term. The fermion sign problem generically prevents Monte Carlo studies of this model on larger systems. However, in the $t=J=0$ limit, the Hamiltonian becomes sign free. Using Green's function Monte Carlo, we investigate the phase diagram of this ring-exchange only fermionic model as a function of density. In this talk, we report our findings.