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<p>In the past two decades, the tools of quantum information theory such as entanglement and correlation are applied to investigate quantum phase transitions (QPT). Quantum steering ellipsoids (QSEs) can serve as a useful geometric tool for describing the strength and type of quantum correlations between two subsystems of a compound system. We concentrate on unveiling how QSE reveals QPT in the XXZ model via quantum renormalization-group method. The results indicate that the QPT are well visualized on the shape of QSE, i.e., it is an oblate spheroid in the spin-fluid phase and degenerate to a point in the Néel phase. Besides, by carrying out enough iterations of the renormalization, the QSE volume <i>V</i> can form two certain values at the critical points, which are linked to two different phases: the spin-fluid phase and the Néel phase. Additionally, we also find that as the system is spin-fluid phase, the volume of QSE between block–block is equal to <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11128_2025_4807_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="36" /> </InlineMediaObject> <EquationSource Format="TEX">\(4\pi /3\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>4</mn> <mi>π</mi> <mo stretchy="false">/</mo> <mn>3</mn> </mrow> </math></EquationSource> </InlineEquation>, which indicates the system must be entangled. In comparison, no entanglement is present in Néel phase because of the volume of QSE between block–block being 0. Furthermore, when the continuous phase transition occurs, there are fluctuations of various scales in the system, and the range of fluctuations is described by the correlation length, which is one of the most important physical quantities in QPT. The result illustrates that the nonanalytic behavior and scaling behaviors of the QSE volume <i>V</i> in the vicinity of the critical point is governed by the exponent which is the inverse of correlation length exponent. Our findings convince us that QSE is capable to signal QPT and is therefore essential for condensed matter physics.</p>

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Quantum steering ellipsoids as visualization signature of quantum phase transition in the XXZ model

  • 期刊论文

  • 发表日期：

    2025年6月17日

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  • Cheng-Cheng Liu,
  • Ze-wei Sun,
  • Xiao-Gang Fan,
  • Zhi-Yong Ding,
  • Ming-Ming Du,
  • Ze-Qing Guo,
  • Juan He,
  • Tao Wu,
  • Liu Ye

摘要

In the past two decades, the tools of quantum information theory such as entanglement and correlation are applied to investigate quantum phase transitions (QPT). Quantum steering ellipsoids (QSEs) can serve as a useful geometric tool for describing the strength and type of quantum correlations between two subsystems of a compound system. We concentrate on unveiling how QSE reveals QPT in the XXZ model via quantum renormalization-group method. The results indicate that the QPT are well visualized on the shape of QSE, i.e., it is an oblate spheroid in the spin-fluid phase and degenerate to a point in the Néel phase. Besides, by carrying out enough iterations of the renormalization, the QSE volume V can form two certain values at the critical points, which are linked to two different phases: the spin-fluid phase and the Néel phase. Additionally, we also find that as the system is spin-fluid phase, the volume of QSE between block–block is equal to \(4\pi /3\) 4 π / 3 , which indicates the system must be entangled. In comparison, no entanglement is present in Néel phase because of the volume of QSE between block–block being 0. Furthermore, when the continuous phase transition occurs, there are fluctuations of various scales in the system, and the range of fluctuations is described by the correlation length, which is one of the most important physical quantities in QPT. The result illustrates that the nonanalytic behavior and scaling behaviors of the QSE volume V in the vicinity of the critical point is governed by the exponent which is the inverse of correlation length exponent. Our findings convince us that QSE is capable to signal QPT and is therefore essential for condensed matter physics.