  We present a Quantum Monte Carlo study of a hardcore boson model with
ring-only exchanges on a square lattice, where a $K_1$ term acts on 1$\times$1
plaquettes and a $K_2$ term acts on 1$\times$2 and 2$\times$1 plaquettes. At
half-filling, the phase diagram reveals charge density wave for small $K_2$,
valence bond solid for intermediate $K_2$, and possibly for large $K_2$ the
novel Exciton Bose Liquid (EBL) phase first proposed by Paramekanti, et
al[Phys. Rev. B {\bf 66}, 054526 (2002)]. Away from half-filling, the EBL phase
is present already for intermediate $K_2$ and remains stable for a range of
densities below 1/2 before phase separation sets in at lower densities
