Entanglement entropy of annulus in three dimensions

Open Access
Regular Article - Theoretical Physics


The entanglement entropy of an annulus is examined in a three-dimensional system with or without a gap. For a free massive scalar field theory, we numerically calculate the mutual information across an annulus. We also study the holographic mutual information in the CGLP background describing a gapped field theory. We discover four types of solutions as the minimal surfaces for the annulus and classify the phase diagrams by varying the inner and outer radii. In both cases, we find the mutual information satisfies the monotonicity dictated by the unitarity and decays exponentially fast as the gap scale is increased. We speculate this is a universal behavior in any gapped system.


Field Theories in Lower Dimensions AdS-CFT Correspondence Lattice Quantum Field Theory 


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Copyright information

© The Author(s) 2015

Authors and Affiliations

  1. 1.Kavli Institute for the Physics and Mathematics of the Universe (WPI)The University of TokyoKashiwa CityJapan
  2. 2.Department of Physics, Faculty of ScienceThe University of TokyoTokyoJapan

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