Abstract
$High-T_c $ Cuprates have been studied quite often as an effective one band $t - J$model that neglects charge fluctuation between oxygen $2p^6$ band and copper$3d^{10}$ band. However, recent Scanning Tunneling Spectra(STS) measurement on underdoped Cuprate shows that charge transfer gap is only of order 1-2eV. This small gap necessitates a re-examination of the charge transfer fluctuation. Here we modify the t-J model by including charge transfer fluctuation. The new model allowing the hopping that forms of doubly occupied sites(doublons) and hopping of doublon. For the same hopping amplitude it is exactly the same with the t-J-U model. This model is studied via variational Monte Carlo method(VMC). The anti-correlation between charge transfer gap and pairing is also confirmed. More interestingly the charge fluctuation is found to affect pairing order parameter in different ways in underdoped and overdoped regions.