We use the notion of  entanglement, and its measures, to get a newer and deeper insight on the  phenomenon of Quantum Phase Transitions (QPTs), i.e. phase transitions  occurring in quantum systems at vanishing temperature. In particular, We  consider the Hubbard model with bond charge interaction $x$ (Hisrch  Model). As a first result [1], we reproduce the exact phase  iagram for  x=1 --integrable case-- by means of measures of entanglemet (Single  and Two-site Von Neumann Entropy, Quantum Mutual Information,  Negativity, Purity). Moreover [2], in the non integrable case $x \neq  1$, we investigate at half filling the superconductor-insulator QPT. The  study is performed by means of a composite analysis of the numerical  results obtained within Density-Matrix Renormalization Group algorithm;  on the one hand, the charge gap closure is studied by standard finite  size scaling analysis; on the other hand we look at singularities in the  derivatives of single-site entanglement. The results of the two  techniques perfectly agree for x >0.5, showing that the validity of  the results obtained by bosonization technique ceases in this region:  the transition takes place at a finite Coulomb interaction u_c.  Numerical extimations of binding energy, spin gap and pairing  correlations are then exploited to characterize the superconducting  nature of the region below $u_c$.
 

 [1] A. Anfossi, P. Giorda, A. Montorsi and F. Traversa:  Two-point vs multipartite entanglement in Quantum Phase Transitions,  preprint cond-mat/0502500.

[2] A. Anfossi, C. Degli Esposti Boschi, A.  Montorsi, F. Ortolani: Single-site entaglement at  ^Superconductor-insulator transition in the Hirsch model, preprint
cond-mat/0503600.