Visualizing quantum phase transitions in the XXZ model via the quantum steering ellipsoid

TL;DR

This paper demonstrates how the quantum steering ellipsoid, a geometric tool, can visually reveal quantum phase transitions in the XXZ model by showing shape changes corresponding to different phases.

Contribution

It introduces the use of the quantum steering ellipsoid to detect QPTs in the XXZ model, providing a geometric perspective on quantum correlations at critical points.

Findings

QSE shape changes at phase transitions

Needle shape in ferromagnetic phase

Oblate spheroid in gapless phase

Abstract

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.