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.

• Received 19 May 2021
• Accepted 8 July 2021

DOI:https://doi.org/10.1103/PhysRevA.104.012418