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  1. We report results of large-scale ground-state density matrix renormalization group (DMRG) calculations on t-t-J cylinders with circumferences 6 and 8. We determine a rough phase diagram that appears to approximate the two-dimensional (2D) system. While for many properties, positive and negativetvalues (t/t=±0.2) appear to correspond to electron- and hole-doped cuprate systems, respectively, the behavior of superconductivity itself shows an inconsistency between the model and the materials. Thet<0(hole-doped) region shows antiferromagnetism limited to very low doping, stripes more generally, and the familiar Fermi surface of the hole-doped cuprates. However, we findt<0strongly suppresses superconductivity. Thet>0(electron-doped) region shows the expected circular Fermi pocket of holes around the(π,π)point and a broad low-doped region of coexisting antiferromagnetism and d-wave pairing with a triplet p component at wavevector(π,π)induced by the antiferromagnetism and d-wave pairing. The pairing for the electron low-doped system witht>0is strong and unambiguous in the DMRG simulations. At larger doping another broad region with stripes in addition to weaker d-wave pairing and striped p-wave pairing appears. In a small doping region nearx=0.08fort0.2, we find an unconventional type of stripe involving unpaired holes located predominantly on chains spaced three lattice spacings apart. The undopedmore »two-leg ladder regions in between mimic the short-ranged spin correlations seen in two-leg Heisenberg ladders.

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