  The past two decades have witnessed a surge of interest in borrowing tools
from quantum information theory to investigate quantum phase transitions
(QPTs). The best known examples are entanglement measures whose
nonanalyticities at critical points were tied to QPTs in a plethora of physical
models. Here, focusing on the XXZ model, we show how QPTs can be revealed
through the quantum steering ellipsoid (QSE), which is a geometric tool capable
of characterizing both the strength and type of quantum correlations between
two subsystems of a compound system. We find that the QSE associated with the
XXZ model changes in shape with the QPTs, that is, it is a needle in the
ferromagnetic phase, an oblate spheroid in the gapless phase, and a prolate
spheroid in the antiferromagnetic phase. This finding offers an example
demonstrating the intriguing possibility of unveiling QPTs in a geometrically
visible fashion. Some connections between our results and previous ones are
discussed.
