Competing And Cooperating Orders In The Three-Band Hubbard Model: A Comprehensive Quantum Monte Carlo And Generalized Hartree-Fock Study

Significant progress has been made in studying strongly correlated electronic systems with major focus on understanding high-temperature superconductivity. At the center of these studies are the so-called cuprates, which are characterized by a quasi-2D Copper-Oxide plane in which superconductivity is believed to arise. From the theoretical point of view, the complex electronic structure of these materials makes a fully ab initio many-body computation a formidable task, so we are forced to focus on minimal models that can reproduce the physics, the most well known of which is known as the Hubbard Model, which relies on the Zhang-Rice singet notion to reduce the degrees of freedom by treating the oxygen atoms implicitly. However, despite years of study, the superconducting order is still unknown. Moreover, recent experiments indicate that the oxygen p-bands play a significant role as non-trivial hole carriers, so we find it fit to study the three-band Hubbard (Emery) model, which treats the oxygen p-orbitals explicitly. We perform extensive generalized Hartree–Fock and auxiliary-field quantum Monte Carlo (AFQMC) calculations for the three-band Hubbard (Emery) model in the underdoped regime, in order to study the ground-state properties of Copper-Oxygen planes in the cuprates. Firstly, we find it important to 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. Secondly, we use these results to guide and feed into exact methods by 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-consistent scheme interfaced 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 results on the charge order, spin order, and localization properties as a function of charge-transfer energ