  The Copper-Oxygen planes in cuprates have been at the center of the search
for a theory of high-temperature superconductivity. We conduct an extensive
study of the ground state of the three-band Hubbard (Emery) model in the
underdoped regime. We focus on the magnetic and charge orders, and present
results from generalized Hartree-Fock (GHF) calculations. The ground-state
properties at the thermodynamic limit are challenging to pin down because of
sensitivity to computational details including the shapes and sizes of the
supercells. We employ large-scale computations with various technical
improvements to determine the orders within GHF. The ground state exhibits a
rich phase diagram with hole doping as the charge transfer energy is varied,
including ferromagnetic domain walls embedded in an antiferromagnetic
background, spin spirals, and nematic order.
