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Entanglement in Nonunitary Quantum Critical Spin Chains

机译：非单位量子临界自旋链的纠缠

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摘要

Entanglement entropy has proven invaluable to our understanding of quantum criticality. It is natural to try to extend the concept to "nonunitary quantum mechanics," which has seen growing interest from areas as diverse as open quantum systems, noninteracting electronic disordered systems, or nonunitary conformal field theory (CFT). We propose and investigate such an extension here, by focusing on the case of one-dimensional quantum group symmetric or supergroup symmetric spin chains. We show that the consideration of left and right eigenstates combined with appropriate definitions of the trace leads to a natural definition of Renyi entropies in a large variety of models. We interpret this definition geometrically in terms of related loop models and calculate the corresponding scaling in the conformal case. This allows us to distinguish the role of the central charge and effective central charge in rational minimal models of CFT, and to define an effective central charge in other, less well-understood cases. The example of the sl(2|1) alternating spin chain for percolation is discussed in detail.
机译：纠缠熵被证明对我们对量子临界性的理解具有无价的作用。尝试将概念扩展到“非单位量子力学”是很自然的，这已引起来自开放量子系统，非相互作用电子无序系统或非单位共形场论（CFT）等领域的越来越多的关注。我们通过关注一维量子组对称或超组对称自旋链的情况，在此提出并研究这种扩展。我们表明，对左本征态和右本征态的考虑与适当的轨迹定义相结合，可以在多种模型中自然地定义Renyi熵。我们根据相关的回路模型以几何方式解释此定义，并在保形情况下计算相应的缩放比例。这使我们能够在合理的CFT最小模型中区分中心收费和有效中心收费的作用，并在其他不太容易理解的情况下定义有效中心收费。详细讨论了用于渗滤的sl（2 | 1）交替自旋链的示例。

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  • 来源
    《Physical review letters》 |2017年第4期|040601.1-040601.5|共5页
  • 作者

    Couvreur Romain; Jacobsen Jesper Lykke; Saleur Hubert;

  • 作者单位

    UPMC Univ Paris 06, PSL Res Univ, Ecole Normale Super, Dept Phys ENS,Lab Physique Theor,CNRS, F-75005 Paris, France|CEA Saclay, Inst Phys Theor, F-91191 Gif Sur Yvette, France;

    UPMC Univ Paris 06, PSL Res Univ, Ecole Normale Super, Dept Phys ENS,Lab Physique Theor,CNRS, F-75005 Paris, France|UPMC Univ Paris 06, Sorbonne Univ, Ecole Normale Super, CNRS,LPT,ENS, F-75005 Paris, France|CEA Saclay, Inst Phys Theor, F-91191 Gif Sur Yvette, France;

    CEA Saclay, Inst Phys Theor, F-91191 Gif Sur Yvette, France|Univ Southern Calif, Dept Phys & Astron, Los Angeles, CA 90089 USA;

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