Doping dependence of bose condensation energy and correlations with spectral peak intensity and superfluid weight in high Tc cuprates

Based on our recent holon-pair boson theory of the t-J Hamiltonian (Phys. Rev. B 64, 052501 (2001)) we report the doping dependence of the bose condensation energy, superfluid weight and spectral peak intensity. We find a universality of doping dependence in these physical quantities, by equally showing an arch shape in the variations of their magnitudes with the hole doping concentration. We find that all of these physical quantities scale well with the positive charge carrier (hole) density x, but not with the electron density 1-x for the entire range of hole doping. It is shown that the doping dependence of the condensation energy U at T = 0 K is given by the relation, $U(0) \approx \alpha x^2 |\Delta_0|^2$ with $\Delta_0$, the pairing gap at 0 K and $\alpha$, a constant.