Low-lying one-particle anomalous excitations are studied for Gutzwiller
projected strongly correlated BCS states. It is found that the one-particle
anomalous excitations are highly coherent, and the numerically calculated
spectrum can be reproduced quantitatively by a renormalized BCS theory, thus
strongly indicating that the nature of low-lying excitations described by the
projected BCS states is essentially understood within a renormalized Bogoliubov
quasi-particle picture. This finding resembles a well known fact that a
Gutzwiller projected Fermi gas is a Fermi liquid. The present results are
consistent with numerically exact calculations of the two-dimensional t-J model
as well as recent photoemission experiments on high-T_{\rm C} cuprate
superconductors.Comment: 5 pages, 3 figures, accepted for publication in Phys. Rev. B 74,
180504(R) (2006