Charge density correlations in $t-J$ ladders investigated by the contractor-renormalization method

Using four-site plaquette or rung basis decomposition, the contractor-renormalization method is applied to two-leg and four-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. Spin gaps, pair-binding energies, and charge correlations are computed and compared to available exact-diagonalization and density-matrix renormalization-group data for the full Hamiltonian. Strong evidence for short-range diagonal stripe correlations are found in periodic four-leg $t-J$ ladders.