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Typical Wannier-function downfolding starts with a mean-field or density functional set of bands to construct the Wannier functions. Here we carry out a controlled approach, using DMRG-computed natural orbital bands, to downfold the three-band Hubbard model to an effective single band model. A sharp drop-off in the natural orbital occupancy at the edge of the first band provides a clear justification for a single-band model. Constructing Wannier functions from the first band, we compute all possible two-particle terms and retain those with significant magnitude. The resulting single-band model includes two-site density-assisted hopping terms with tn∼0.6t. These terms lead to a reduction of the ratio U/teff, and are important in capturing the doping-asymmetric carrier mobility, as well as in enhancing the pairing in a single-band model for the hole-doped cuprates.more » « less
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We report results of large-scale ground-state density matrix renormalization group (DMRG) calculations on 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 negative values ( ) 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. The (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 find strongly suppresses superconductivity. The (electron-doped) region shows the expected circular Fermi pocket of holes around the point and a broad low-doped region of coexisting antiferromagnetism and d-wave pairing with a triplet p component at wavevector induced by the antiferromagnetism and d-wave pairing. The pairing for the electron low-doped system with is 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 near for , we find an unconventional type of stripe involving unpaired holes located predominantly on chains spaced three lattice spacings apart. The undoped two-leg ladder regions in between mimic the short-ranged spin correlations seen in two-leg Heisenberg ladders.