  Using 4-site plaquette or rung basis decomposition, the CORE method is
applied to 2-leg and 4-leg t-J ladders and cylinders. Resulting range-2
effective hamiltonians are studied numerically on periodic rings taking full
advantage of the translation symmetry as well as the drastic reduction of the
Hilbert space. We investigate the role of magnetic and fermionic degrees of
freedom to obtain the most reliable representation of the underlying model.
Spin gaps, pair binding energies and charge correlations are computed and
compared to available ED and DMRG data for the full Hamiltonian. Strong
evidences for short-range diagonal stripe correlations are found in periodic
4-leg t-J ladders.
