# The MFA ground states for the extended Bose-Hubbard model with a three-body constraint

## TL;DR

This paper investigates the ground states of an extended Bose-Hubbard model with a three-body constraint using mean-field and quantum Monte Carlo methods, revealing phase behaviors relevant to high-Tc cuprates.

## Contribution

It introduces a generalized mean-field and quantum Monte Carlo analysis of the 2D S=1 system with a three-state on-site Hilbert space, connecting to high-Tc cuprate models.

## Key findings

- Identification of ground state phases under doping variations
- Demonstration of model equivalence to an anisotropic S=1 quantum magnet
- Insights into charge degrees of freedom in cuprate-like systems

## Abstract

We address the intensively studied extended bosonic Hubbard model (EBHM) with truncation of the on-site Hilbert space to the three lowest occupation states n=0,1,2 in frames of the S=1 pseudospin formalism. Similar model was recently proposed to describe the charge degree of freedom in a model high-Tc 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 with a two-particle transport to find the ground state phase with its evolution under deviation from half-filling.