### Abstract

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.

Original language | English |
---|---|

Article number | 116 |

Journal | Journal of High Energy Physics |

Volume | 2016 |

Issue number | 11 |

DOIs | |

Publication status | Published - 2016 Nov 1 |

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### Keywords

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

### ASJC Scopus subject areas

- Nuclear and High Energy Physics

### Cite this

*Journal of High Energy Physics*,

*2016*(11), [116]. https://doi.org/10.1007/JHEP11(2016)116

**Thermality and excited state Rényi entropy in two-dimensional CFT.** / Lin, Feng Li; Wang, Huajia; Zhang, Jia ju.

Research output: Contribution to journal › Article

*Journal of High Energy Physics*, vol. 2016, no. 11, 116. https://doi.org/10.1007/JHEP11(2016)116

}

TY - JOUR

T1 - Thermality and excited state Rényi entropy in two-dimensional CFT

AU - Lin, Feng Li

AU - Wang, Huajia

AU - Zhang, Jia ju

PY - 2016/11/1

Y1 - 2016/11/1

N2 - 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.

AB - 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.

KW - AdS-CFT Correspondence

KW - Conformal Field Theory

KW - Holography and condensed matter physics (AdS/CMT)

UR - http://www.scopus.com/inward/record.url?scp=84996489733&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84996489733&partnerID=8YFLogxK

U2 - 10.1007/JHEP11(2016)116

DO - 10.1007/JHEP11(2016)116

M3 - Article

AN - SCOPUS:84996489733

VL - 2016

JO - Journal of High Energy Physics

JF - Journal of High Energy Physics

SN - 1126-6708

IS - 11

M1 - 116

ER -