Multiorbital Cu impurity embedded in an anisotropic square lattice of oxygen atoms

Motivated by the recent experimental findings on the orbital ordering of cuprate superconductors (SC), we investigated the multiorbital Cu impurity including local exchange and Coulomb interactions embedded in the O lattice by incorporating the $3{d}^{8}$ multiplet structure coupled to a full O-$2p$ band. Instead of providing physical mechanism of this spontaneous symmetry breaking, we systematically investigate the impact of artificial anisotropy of various parameters to reveal rich phenomena in terms of the ground-state (GS) weight asymmetry between the $\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{x}$ and $\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{y}$ directions. The numerical evidence demonstrates that the GS weight of the Zhang-Rice singlet (ZRS) can be affected by the asymmetry of these parameters to distinct extent. Although the experimentally motivated asymmetric charge transfer energy only induces a tiny weight difference, the asymmetric $d\text{\ensuremath{-}}p$ hybridization can result in considerable asymmetry of the GS weight, which also intriguingly shows that the critical charge transfer energy separating the $^{1}A_{1}$ singlet and $^{3}B_{1}$ triplet GS is independent of the intermediate asymmetry ratio regime. More importantly, the nearest-neighbor (NN) ${V}_{pd}$ has much stronger impact than the local ${U}_{pp}$, which stems from the nature of ZRS consisting of nearest-neighbor two holes. Our systematic exploration provides valuable knowledge on the role of the artificial symmetry breaking on the two-hole GS nature and serves as the starting point of more sophisticated many-body simulations to uncover more interesting physics of the multiorbital Cu lattice model within the symmetry breaking setup.