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We analyze a class of mean-field (MF) lattice-fermion Hamiltonians andconstruct the corresponding grand-canonical density operator for such system.New terms are introduced, which may be interpreted as local fugacities,molecular fields, etc. The presence of such terms is an unavoidable consequenceof a consistent statistical description. Although in some cases (e.g. in theHartree or the Hartree-Fock-type approximation) the presented formalism isredundant, in general (e.g. for a renormalized t-J model) it leads tonontrivial modifications of the thermodynamic properties.

Construction of density operator for a general mean-field Hamiltonian and its application to the models of correlated fermions