Density-matrix-renormalization-group-based downfolding of the three-band Hubbard model: the importance of density-assisted hopping

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 $t_n\sim 0.6t$. These terms lead to a reduction of the ratio $U\mathrm{/}{t}_{\mathrm{e}\mathrm{f}\mathrm{f}}$, 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.