Ground-state properties of the three-band Hubbard model

The three-band Hubbard model proposed by Emery describes the CuO$_2$ plane in cuprate superconductors by retaining both Cu and O orbitals in a minimal sense. Applying the latest developments in the auxiliary-field quantum Monte Carlo (AFQMC) method, we investigate ground-state properties of this model at half-filling and when lightly (under-)doped. The AFQMC uses generalized Hartree-Fock (GHF) trial wave functions to control the sign problem. A self-consistent constraint \footnote{M.\ Qin, H.\ Shi, S.\ Zhang, arXiv:1608.07154 (2016).} is applied. We also determine the unrestricted Hartree-Fock (UHF) and GHF ground states and compare their predictions with those from AFQMC. Similarities and differences between the three-band model and one-band Hubbard model will be discussed.