Journal of High Energy Physics

, 2016:116 | Cite as

Thermality and excited state Rényi entropy in two-dimensional CFT

Open Access
Regular Article - Theoretical Physics


We evaluate one-interval Rényi entropy and entanglement entropy for the excited states of two-dimensional conformal field theory (CFT) on a cylinder, and examine their differences from the ones for the thermal state. We assume the interval to be short so that we can use operator product expansion (OPE) of twist operators to calculate Rényi entropy in terms of sum of one-point functions of OPE blocks. We find that the entanglement entropy for highly excited state and thermal state behave the same way after appropriate identification of the conformal weight of the state with the temperature. However, there exists no such universal identification for the Rényi entropy in the short-interval expansion. Therefore, the highly excited state does not look thermal when comparing its Rényi entropy to the thermal state one. As the Rényi entropy captures the higher moments of the reduced density matrix but the entanglement entropy only the average, our results imply that the emergence of thermality depends on how refined we look into the entanglement structure of the underlying pure excited state.


Conformal Field Theory AdS-CFT Correspondence Holography and condensed matter physics (AdS/CMT) 


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Copyright information

© The Author(s) 2016

Authors and Affiliations

  1. 1.Department of PhysicsNational Taiwan Normal UniversityTaipeiTaiwan
  2. 2.Department of PhysicsUniversity of IllinoisUrbana-ChampaignU.S.A.
  3. 3.Dipartimento di FisicaUniversità degli Studi di Milano-BicoccaMilanoItaly
  4. 4.Theoretical Physics Division, Institute of High Energy PhysicsChinese Academy of SciencesBeijingP.R. China
  5. 5.Theoretical Physics Center for Science FacilitiesChinese Academy of SciencesBeijingP.R. China

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