Journal of High Energy Physics

, 2015:203 | Cite as

Holographic entropy inequalities and gapped phases of matter

  • Ning Bao
  • ChunJun CaoEmail author
  • Michael Walter
  • Zitao Wang
Open Access
Regular Article - Theoretical Physics


We extend our studies of holographic entropy inequalities to gapped phases of matter. For any number of regions, we determine the linear entropy inequalities satisfied by systems in which the entanglement entropy satisfies an exact area law. In particular, we find that all holographic entropy inequalities are valid in such systems. In gapped systems with topological order, the “cyclic inequalities” derived recently for the holo-graphic entanglement entropy generalize the Kitaev-Preskill formula for the topological entanglement entropy. Finally, we propose a candidate linear inequality for general 4-party quantum states.


AdS-CFT Correspondence Holography and condensed matter physics (AdS/CMT) Topological States of Matter 


Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.


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Copyright information

© The Author(s) 2015

Authors and Affiliations

  • Ning Bao
    • 1
    • 2
  • ChunJun Cao
    • 2
    Email author
  • Michael Walter
    • 3
  • Zitao Wang
    • 1
    • 2
  1. 1.Institute for Quantum Information and Matter, California Institute of TechnologyPasadenaUnited States
  2. 2.Walter Burke Institute for Theoretical Physics, California Institute of TechnologyPasadenaUnited States
  3. 3.Stanford Institute for Theoretical PhysicsStanford UniversityStanfordUnited States

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