The S=1 pseudospin formalism was recently proposed to describe the charge degree of freedom in a model high-T_{c} cuprate with the on-site Hilbert space reduced to the three effective valence centers, nominally Cu^{1+;2+;3+}. With small corrections the model becomes equivalent to a strongly anisotropic S=1 quantum magnet in an external magnetic field. We have applied a generalized mean-field approach and quantum Monte-Carlo technique for the model 2D S=1 system to find the ground state phase with its evolution under deviation from half-filling and different correlation functions. Special attention is given to the role played by the on-site correlation ("single-ion anisotropy").
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