Magnetic and charge orders in the ground state of the Emery model: Accurate numerical results

We perform extensive auxiliary-field quantum Monte Carlo (AFQMC) calculations for the three-band Hubbard (Emery) model in order to study the ground-state properties of copper-oxygen planes in the cuprates. Employing cutting-edge AFQMC techniques with a self-consistent gauge constraint in auxiliary-field space to control the sign problem, we reach supercells containing ≈ 500 atoms to capture collective modes in the charge and spin orders and characterize the behavior in the thermodynamic limit. The self-consistency scheme interfacing with generalized Hartree-Fock calculations allows high accuracy in AFQMC to resolve small energy scales, which is crucial for determining the complex candidate orders in such a system. We present detailed information on the charge order, spin order, momentum distribution, and localization properties as a function of charge-transfer energy for the the underdoped regime. In contrast with the stripe and spiral orders under hole doping, we find that the corresponding 1/8 electron-doped system exhibits purely antiferromagnetic order in the three-band model, consistent with the asymmetry between electron and hole doping in the phase diagram of cuprates.