  The role of two-point and multipartite entanglement at quantum phase
transitions (QPTs) in correlated electron systems is investigated. We consider
a bond-charge extended Hubbard model exactly solvable in one dimension which
displays various QPTs, with two (qubit) as well as more (qudit) on-site degrees
of freedom involved. The analysis is carried out by means of appropriate
measures of bipartite/multipartite quantum correlations. It is found that all
transitions ascribed to two-point correlations are characterized by an
entanglement range which diverges at the transition points. The exponent
coincides with that of the correlation length at the transitions. We introduce
the correlation ratio, namely, the ratio of quantum mutual information and
single-site entanglement. We show that at T=0, it captures the relative role of
two-point and multipartite quantum correlations at transition points,
generalizing to qudit systems the entanglement ratio. Moreover, a finite value
of quantum mutual information between infinitely distant sites is seen to
quantify the presence of off-diagonal long-range order induced by multipartite
entanglement.
