  We have developed a new approach based on matrix product representations of
ground states to study Quantum Phase Transitions (QPT). As confirmation of the
power of our approach we have analytically analyzed the XXZ spin-one chain with
uniaxial single-ion-type anisotropy and our results compare favourably with
previous numerical studies. In addition, our description lets to know which
part of parameters space of the Hamiltonian is most likely to be exactly
solvable.
