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

Failure of Gutzwiller-type wave function to capture gauge fluctuations: Case study in the Exciton Bose Liquid context