Evolution of entanglement wedge cross section following a global quench
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Springer
Received: May Revised: July Accepted: July Published: August
21, 19, 24, 25,
2020 2020 2020 2020
Komeil Babaei Velni,a,b,d M. Reza Mohammadi Mozaffara,b and M.H. Vahidiniac,b a
Department of Physics, University of Guilan, P.O. Box 41335-1914, Rasht, Iran b School of Physics, Institute for Research in Fundamental Sciences (IPM), P.O. Box 19395-5531, Tehran, Iran c Department of Physics, Institute for Advanced Studies in Basic Sciences (IASBS), P.O. Box 45137-66731, Zanjan, Iran d School of Particles and Accelerators, Institute for Research in Fundamental Sciences (IPM), P.O. Box 19395-5531, Tehran, Iran
E-mail: [email protected], [email protected], [email protected] Abstract: We study the evolution of entanglement wedge cross section (EWCS) in the Vaidya geometry describing a thin shell of null matter collapsing into the AdS vacuum to form a black brane. In the holographic context, it is proposed that this quantity is dual to different information measures including entanglement of purification, reflected entropy, odd entropy and logarithmic negativity. In 2 + 1 dimensions, we present a combination of numerical and analytic results on the evolution and scaling of EWCS for strip shaped boundary subregions after a thermal quench. In the limit of large subregions, we find that the time evolution of EWCS is characterized by three different scaling regimes: an early time quadratic growth, an intermediate linear growth and a late time saturation. Further, in 3 + 1 dimensions, we examine the scaling behavior by considering thermal and electromagnetic quenches. In the case of a thermal quench, our numerical analysis supply results similar to observations made for the lower dimension. On the other hand, for electromagnetic quenches at zero temperature, an interesting feature is a departure from the linear behavior of the evolution to logarithmic growth. Keywords: AdS-CFT Correspondence, Gauge-gravity correspondence, Holography and condensed matter physics (AdS/CMT) ArXiv ePrint: 2005.05673
c The Authors. Open Access, Article funded by SCOAP3 .
https://doi.org/10.1007/JHEP08(2020)129
JHEP08(2020)129
Evolution of entanglement wedge cross section following a global quench
Contents 1 Introduction
1
2 Set-up
5 9 9 11
4 EWCS in Vaidya backgrounds: 2 + 1 dimensions 4.1 Numerical analysis 4.2 Analytic treatment 4.3 Regimes in the growth of EWCS
12 12 15 20
5 EWCS in Vaidya backgrounds: higher dimensions 5.1 Evolution after a thermal quench (q = 0) 5.2 Evolution after a electromagnetic quench (q 6= 0)
23 23 24
6 Conclusions and discussions
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1
Introduction
Non-equilibrium dynamics and thermalization of a strongly coupled system is a longstanding problem in many areas of physics. In the holographic context, equilibration from a highly excited initial state is expected to be dual to black hole formation under a gravitational collapse. So in this scenario, issues about the black hole physics are tightly connected to the physics of thermalization in the dual strongly coupled system [1] (
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