  Slave particle approaches are widely used in studies of exotic quantum
phases. A complete description beyond mean field also contains dynamical gauge
fields, while a simplified procedure considers Gutzwiller-projected trial
states. We apply this in the context of bosonic models with ring exchanges
realizing so-called Exciton Bose Liquid (EBL) phase and compare a Gutzwiller
wave function against an accurate EBL wave function. We solve the parton-gauge
theory and show that dynamical fluctuations of the spatial gauge fields are
necessary for obtaining qualitatively accurate EBL description. On the
contrary, just the Gutzwiller projection leads to a state with subtle
differences in the long-wavelength properties, thus suggesting that Gutzwiller
wave functions may generally fail to capture long-wavelength physics.
