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