Pseudospin S=1 description of the cuprate complexity: the charge triplets model

We introduce a minimal model for 2D cuprates with the on-site Hilbert space reduced to only three effective valence centers CuO$_4^{7-,6-,5-}$ (nominally Cu$^{1+,2+,3+}$) and make use of the S=1 pseudospin formalism. Despite its seeming simplicity the model is believed to capture the salient features both of the hole- and electron-doped cuprates. The pseudospin formalism elucidates an unique fermion-boson duality of the doped cuprates, does provide an unified standpoint for classification of the "myriad"\, of electronic phases in cuprates and the evolution of the CuO$_2$ planes under a nonisovalent doping, introduces the on-site mixed valence quantum superpositions and order parameters to be novel features of the cuprate physics, does provide a comprehensive description of the correlated one- and two-particle transport, coexistence of $p$- and $n$-type carriers, electron-hole asymmetry, anticorrelation of conventional spin and superconducting order parameters. Concept of the electron and hole centers, differing by a composite local boson, and electron-hole pairing are shown to explain central points of the cuprate puzzles, in particular, the HTSC itself, pseudogap, and Fermi surface reconstruction.