TY - JOUR
T1 - Note on ETH of descendant states in 2D CFT
AU - Guo, Wu zhong
AU - Lin, Feng Li
AU - Zhang, Jiaju
N1 - Funding Information:
We would like thank Pasquale Calabrese, Chong-Sun Chu, Hong Liu, Erik Tonni for helpful discussions. We thank the anonymous referee for valuable comments and suggestions. WZG would like to thank the physics department of Jinan University for hospitality where part of this work was completed. JZ would like to thank the Galileo Galilei Institute for Theoretical Physics and the organisers of the workshop “Entanglement in Quantum Systems” for hospitality and to thank participants of the workshop for helpful discussions. WZG is supported in part by the National Center of Theoretical Science (NCTS). FLL is supported by Taiwan Ministry of Science and Technology through Grant No. 103-2112-M-003-001-MY3. JZ is supported by Fondazione Cariplo and Regione Lombardia through Grant No. 2015-1253, and by ERC Consolidator Grant No. 771536 (NEMO).
PY - 2019/1/1
Y1 - 2019/1/1
N2 - We investigate the eigenstate thermalization hypothesis (ETH) of highly excited descendant states in two-dimensional large central charge c conformal field theory. We use operator product expansion of twist operators to calculate the short interval expansions of entanglement entropy and relative entropy for an interval of length ℓ up to order ℓ12. Using these results to ensure ETH of a heavy state when compared with the canonical ensemble state up to various orders of c, we get the constraints on the expectation values of the first few quasiprimary operators in the vacuum conformal family at the corresponding order of c. Similarly, we also obtain the constraints from the expectation values of the first few Korteweg-de Vries charges. We check these constraints for some types of special descendant excited states. Among the descendant states we consider, we find that at most only the leading order ones of the ETH constraints can be satisfied for the descendant states that are slightly excited on top of a heavy primary state. Otherwise, the ETH constraints are violated for the descendant states that are heavily excited on top of a primary state.
AB - We investigate the eigenstate thermalization hypothesis (ETH) of highly excited descendant states in two-dimensional large central charge c conformal field theory. We use operator product expansion of twist operators to calculate the short interval expansions of entanglement entropy and relative entropy for an interval of length ℓ up to order ℓ12. Using these results to ensure ETH of a heavy state when compared with the canonical ensemble state up to various orders of c, we get the constraints on the expectation values of the first few quasiprimary operators in the vacuum conformal family at the corresponding order of c. Similarly, we also obtain the constraints from the expectation values of the first few Korteweg-de Vries charges. We check these constraints for some types of special descendant excited states. Among the descendant states we consider, we find that at most only the leading order ones of the ETH constraints can be satisfied for the descendant states that are slightly excited on top of a heavy primary state. Otherwise, the ETH constraints are violated for the descendant states that are heavily excited on top of a primary state.
KW - AdS-CFT Correspondence
KW - Conformal Field Theory
KW - Gauge-gravity correspondence
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U2 - 10.1007/JHEP01(2019)152
DO - 10.1007/JHEP01(2019)152
M3 - Article
AN - SCOPUS:85060914924
VL - 2019
JO - Journal of High Energy Physics
JF - Journal of High Energy Physics
SN - 1126-6708
IS - 1
M1 - 152
ER -