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The short-range correlations are considered for a two-dimensional hard-coreboson model on square lattice within Bethe approximation for the clustersconsisting of two and four sites. Explicit equations are derived for thecritical temperatures of charge and superfluid ordering and their solutions areconsidered for various ratios of the charge-charge correlation parameter to thetransfer integral. It is shown that taking into account short-rangecorrelations for the temperatures of charge ordering results in the appearanceof the critical concentration of bosons, which restricts the existence domainof the solutions of charge ordering type. In the case of superfluid orderingwith the assumption of short-range correlations, the critical temperature isreduced up to zero values at half-filling. A phase diagram of the hard-coreboson model is constructed with the assumption of phase separation withinMaxwell's construction and it is shown that taking into account short-rangecorrelations within Bethe approximation quantitatively approximates the form ofphase diagram to the results of the quantum Monte Carlo method.

Critical Temperatures of Hard-Core Boson Model on Square Lattice within Bethe Approximation