Effective-field theory for high-$T_c$ cuprates

Starting with a minimal model for the CuO$_2$ planes with the on-site Hilbert space reduced to only three effective valence centers [CuO$_4$]$^{7-,6-,5-}$ (nominally Cu$^{1+,2+,3+}$) with different conventional spin and different orbital symmetry we propose a unified non-BCS model that allows one to describe the main features of the phase diagrams of doped cuprates within the framework of a simple effective field theory.