  Phase diagram of the Hubbard-Holstein model in the coexistence of
electron-electron and electron-phonon interactions has been theoretically
obtained with the density-matrix renormalization group method for
one-dimensional (1D) systems, where an improved warm-up (the recursive sweep)
procedure has enabled us to calculate various correlation functions. We have
examined the cases of (i) the systems half-filled by electrons for the full
parameter space spanned by the electron-electron and electron-phonon coupling
constants and the phonon frequency, (ii) non-half-filled system, and (iii)
trestle lattice. For (i), we have detected a region where both the charge and
on-site pairing correlations decay with power-laws in real space, which
suggests a metallic behavior. While pairing correlations are not dominant in
(i), we have found that they become dominant as the system is doped in (ii), or
as the electronic band structure is modified (with a broken electron-hole
symmetry) in (iii) in certain parameter regions.
