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Gutzwiller-projected BCS wave function or the resonating-valence-bond (RVB)state in the 2D extended t-J model is investigated by using the variationalMonte Carlo technique. We show that the results of ground-state energy andexcitation spectra calculated in the grand-canonical scheme allowing particlenumber to fluctuate are essentially the same as previous results obtained byfixing the number of particle in the canonical scheme if the grandthermodynamic potential is used for minimization. To account for the effect ofGutzwiller projection, a fugacity factor proposed by Laughlin and Anderson fewyears ago has to be inserted into the coherence factor of the BCS state.Chemical potential, particle number fluctuation, and phase fluctuation of theRVB state, difficult or even impossible to be calculated in the canonicalensemble, have been directly measured in the grand-canonical picture. We findthat except for La-214 materials, the doping dependence of chemical potentialis consistent with experimental findings on several cuprates. Similar to whathas been reported by scanning tunneling spectroscopy experiments, the tunnelingasymmetry becomes much stronger as doping decreases. We found a very largeenhancement of phase fluctuation in the underdoped regime.

Grand-canonical variational approach for the t-J model