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Journal of High Energy Physics

, 2018:112 | Cite as

Page curves for general interacting systems

  • Hiroyuki Fujita
  • Yuya O. Nakagawa
  • Sho Sugiura
  • Masataka WatanabeEmail author
Open Access
Regular Article - Theoretical Physics
  • 27 Downloads

Abstract

We calculate in detail the Renyi entanglement entropies of cTPQ states as a function of subsystem volume, filling the details of our prior work [24], where the formulas were first presented. Working in a limit of large total volume, we find universal formulas for the Renyi entanglement entropies in a region where the subsystem volume is comparable to that of the total system. The formulas are applicable to the infinite temperature limit as well as general interacting systems. For example we find that the second Renyi entropy of cTPQ states in terms of subsystem volume is written universally up to two constants, (S2() = − ln K(β) + ln a(β) − ln 1+a(β)L+2), where L is the total volume of the system and a and K are two undetermined constants. The uses of the formulas were already presented in our prior work and we mostly concentrate on the theoretical aspect of the formulas themselves. Aside from deriving the formulas for the Renyi Page curves, the expression for the von Neumann Page curve is also derived, which was not presented in our previous work.

Keywords

Lattice Quantum Field Theory Random Systems Conformal Field Theory 

Notes

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) 2018

Authors and Affiliations

  1. 1.Institute for Solid State PhysicsThe University of TokyoKashiwaJapan
  2. 2.Department of Physics, Faculty of ScienceThe University of TokyoTokyoJapan
  3. 3.Department of PhysicsHarvard UniversityCambridgeU.S.A.
  4. 4.Kavli Institute for the Physics and Mathematics of the Universe (WPI), The University of Tokyo Institutes for Advanced StudyThe University of TokyoKashiwaJapan

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