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Chinese Physics C > 2020, Vol. 44 > Issue(2): 023101 DOI: 10.1088/1674-1137/44/2/023101

Entanglement entropy of an annulus in holographic thermalization

  • 1.

    Institute of High Energy Physics, Chinese Academy of Sciences, Beijing 100049, China

  • 2.

    School of Physics, University of Chinese Academy of Sciences, Beijing 100049, China

  • 3.

    Institute of Theoretical Physics, Chinese Academy of Science, Beijing 100190, China

  • The thermalization process of the holographic entanglement entropy (HEE) of an annular domain is investigated in the Vaidya-AdS geometry. We determine numerically the Hubeny-Rangamani-Takayanagi (HRT) surface, which may be a hemi-torus or two disks, depending on the ratio of the inner radius to the outer radius of the annulus. More importantly, for some fixed ratio of the two radii, the annulus undergoes a phase transition, or a double phase transition, during thermalization from a hemi-torus to a two-disk configuration, or vice versa. The occurrence of various phase transitions is determined by the ratio of the two radii of the annulus. The rate of entanglement growth is also investigated during the thermal quench. The local maximal rate of entanglement growth occurs in the region with a double phase transition. Finally, if the quench process is sufficiently slow, which may be controlled by the thickness of the null shell, the region with a double phase transition vanishes.
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Yi Ling, Yuxuan Liu and Zhuo-Yu Xian. Entanglement entropy of annulus in holographic thermalization[J]. Chinese Physics C. doi: 10.1088/1674-1137/44/2/023101
Yi Ling, Yuxuan Liu and Zhuo-Yu Xian. Entanglement entropy of annulus in holographic thermalization[J]. Chinese Physics C. doi:10.1088/1674-1137/44/2/023101 shu
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Received: 2019-09-29
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    Entanglement entropy of an annulus in holographic thermalization

    • 1. Institute of High Energy Physics, Chinese Academy of Sciences, Beijing 100049, China
    • 2. School of Physics, University of Chinese Academy of Sciences, Beijing 100049, China
    • 3. Institute of Theoretical Physics, Chinese Academy of Science, Beijing 100190, China
    • Received Date:2019-09-29
    • Available Online:2020-02-01

      Abstract:The thermalization process of the holographic entanglement entropy (HEE) of an annular domain is investigated in the Vaidya-AdS geometry. We determine numerically the Hubeny-Rangamani-Takayanagi (HRT) surface, which may be a hemi-torus or two disks, depending on the ratio of the inner radius to the outer radius of the annulus. More importantly, for some fixed ratio of the two radii, the annulus undergoes a phase transition, or a double phase transition, during thermalization from a hemi-torus to a two-disk configuration, or vice versa. The occurrence of various phase transitions is determined by the ratio of the two radii of the annulus. The rate of entanglement growth is also investigated during the thermal quench. The local maximal rate of entanglement growth occurs in the region with a double phase transition. Finally, if the quench process is sufficiently slow, which may be controlled by the thickness of the null shell, the region with a double phase transition vanishes.

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        1. Introduction

        • Entanglement entropy, as a vital tool for measuring the entanglement of quantum systems, has been extensively investigated in recent years. For a strongly coupled quantum system which is in a pure state, the entanglement entropy between the subsystem $ {\cal{A}} $ and its complement $ \bar{{\cal{A}}} $ is proportional to the area of the boundary $ \partial {\cal{A}} $ to the leading order [1]. In the context of AdS/CFT correspondence [2-4], the Ryu-Takayanagi (RT) formula [5,6] conjectures that the entanglement entropy can be evaluated as the area of the minimal surface $ \gamma_{{\cal{A}}} $

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