  We analyze correlations between subsystems for an extended Hubbard model
exactly solvable in one dimension, which exhibits a rich structure of quantum
phase transitions (QPTs). The T=0 phase diagram is exactly reproduced by
studying singularities of single-site entanglement. It is shown how comparison
of the latter quantity and quantum mutual information allows one to recognize
whether two-point or shared quantum correlations are responsible for each of
the occurring QPTs. The method works in principle for any number D of degrees
of freedom per site. As a by-product, we are providing a benchmark for direct
measures of bipartite entanglement; in particular, here we discuss the role of
negativity at the transition.
