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 density matrix renormalization group 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 $t_n\sim 0.6t$. These terms lead to a reduction of the ratio $U/t_{\mathrm{eff}}$, 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.

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• Superconducting phase transition
• Cuprates
• High-temperature superconductors
• Strongly correlated systems
• Density matrix renormalization group
• Wannier function methods