A consistent statistical treatment of the renormalized mean-field t-J model

A variational treatment of the Gutzwiller - renormalized t-J Hamiltonian combined with the mean-field (MF) approximation is proposed, with a simultaneous inclusion of additional consistency conditions. Those conditions guarantee that the averages calculated variationally represent true mean-field expectation values. This is not ensured a priori when the effective Hamiltonian contains renormalization factors which depend on the mean-field averages. A comparison with previous mean-field treatments is made for both superconducting (d-RVB) and normal states and encompasses calculations of both the superconducting gap and the renormalized hopping amplitudes, as well as the electronic structure. The $C_{4v}$-symmetry breaking in the normal phase - the Pomeranchuk instability (PI) - is also analyzed.