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We study the quantum discord (QD) and the classical correlations (CC) in areference model for strongly correlated electrons, the one-dimensionalbond-charge extended Hubbard model. We show that the comparison of QD and CCand of their derivatives in the direct and reciprocal lattice allows one toefficiently inspect the structure of two-point driven quantum phase transitions(QPTs), discriminating those at which off diagonal long range order (ODLRO) isinvolved. Moreover we observe that QD between pair of sites is a monotonicfunction of ODLRO, thus establishing a direct relation between the latter andtwo point quantum correlations different from the entanglement. The study ofthe ground state properties allows to show that for a whole class ofpermutation invariant (\eta-pair) states quantum discord can violate themonogamy property, both in presence and in absence of bipartite entanglement.In the thermodynamic limit, due to the presence of ODLRO, the violation for\eta-pair states is maximal, while for the purely fermionic ground state isfinite. From a general perspective, all our results validate the importance ofthe concepts of QD and CC for the study of critical condensed-matter systems.

physical review. b, condensed matter and materials physics

Quantum discord and classical correlations in the bond-charge Hubbard  model: quantum phase transitions, ODLRO and violation of the monogamy  property for discord