Renyi entropy for local quenches in 2D CFT from numerical conformal blocks
Abstract We study the time evolution of Renyi entanglement entropy for locally excited states in two dimensional large central charge CFTs. It generically shows a logarithmical growth and we compute the coefficient of log t term. Our analysis covers the entire parameter regions with respect to the r...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2018-01-01
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| Series: | Journal of High Energy Physics |
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| Online Access: | http://link.springer.com/article/10.1007/JHEP01(2018)115 |
| _version_ | 1818315743899418624 |
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| author | Yuya Kusuki Tadashi Takayanagi |
| author_facet | Yuya Kusuki Tadashi Takayanagi |
| author_sort | Yuya Kusuki |
| collection | DOAJ |
| description | Abstract We study the time evolution of Renyi entanglement entropy for locally excited states in two dimensional large central charge CFTs. It generically shows a logarithmical growth and we compute the coefficient of log t term. Our analysis covers the entire parameter regions with respect to the replica number n and the conformal dimension h O of the primary operator which creates the excitation. We numerically analyse relevant vacuum conformal blocks by using Zamolodchikov’s recursion relation. We find that the behavior of the conformal blocks in two dimensional CFTs with a central charge c, drastically changes when the dimensions of external primary states reach the value c/32. In particular, when h O ≥ c/32 and n ≥ 2, we find a new universal formula ΔSAn≃nc24n−1 $$ \varDelta {S}_A^{(n)}\simeq \frac{nc}{24\left(n-1\right)} $$ log t. Our numerical results also confirm existing analytical results using the HHLL approximation. |
| first_indexed | 2024-12-13T09:10:24Z |
| format | Article |
| id | doaj.art-938cd948175e4b2399d836a854c2d7f9 |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-12-13T09:10:24Z |
| publishDate | 2018-01-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-938cd948175e4b2399d836a854c2d7f92022-12-21T23:52:58ZengSpringerOpenJournal of High Energy Physics1029-84792018-01-012018112210.1007/JHEP01(2018)115Renyi entropy for local quenches in 2D CFT from numerical conformal blocksYuya Kusuki0Tadashi Takayanagi1Center for Gravitational Physics, Yukawa Institute for Theoretical Physics (YITP), Kyoto UniversityCenter for Gravitational Physics, Yukawa Institute for Theoretical Physics (YITP), Kyoto UniversityAbstract We study the time evolution of Renyi entanglement entropy for locally excited states in two dimensional large central charge CFTs. It generically shows a logarithmical growth and we compute the coefficient of log t term. Our analysis covers the entire parameter regions with respect to the replica number n and the conformal dimension h O of the primary operator which creates the excitation. We numerically analyse relevant vacuum conformal blocks by using Zamolodchikov’s recursion relation. We find that the behavior of the conformal blocks in two dimensional CFTs with a central charge c, drastically changes when the dimensions of external primary states reach the value c/32. In particular, when h O ≥ c/32 and n ≥ 2, we find a new universal formula ΔSAn≃nc24n−1 $$ \varDelta {S}_A^{(n)}\simeq \frac{nc}{24\left(n-1\right)} $$ log t. Our numerical results also confirm existing analytical results using the HHLL approximation.http://link.springer.com/article/10.1007/JHEP01(2018)115AdS-CFT CorrespondenceConformal Field TheoryField Theories in Lower Dimensions |
| spellingShingle | Yuya Kusuki Tadashi Takayanagi Renyi entropy for local quenches in 2D CFT from numerical conformal blocks Journal of High Energy Physics AdS-CFT Correspondence Conformal Field Theory Field Theories in Lower Dimensions |
| title | Renyi entropy for local quenches in 2D CFT from numerical conformal blocks |
| title_full | Renyi entropy for local quenches in 2D CFT from numerical conformal blocks |
| title_fullStr | Renyi entropy for local quenches in 2D CFT from numerical conformal blocks |
| title_full_unstemmed | Renyi entropy for local quenches in 2D CFT from numerical conformal blocks |
| title_short | Renyi entropy for local quenches in 2D CFT from numerical conformal blocks |
| title_sort | renyi entropy for local quenches in 2d cft from numerical conformal blocks |
| topic | AdS-CFT Correspondence Conformal Field Theory Field Theories in Lower Dimensions |
| url | http://link.springer.com/article/10.1007/JHEP01(2018)115 |
| work_keys_str_mv | AT yuyakusuki renyientropyforlocalquenchesin2dcftfromnumericalconformalblocks AT tadashitakayanagi renyientropyforlocalquenchesin2dcftfromnumericalconformalblocks |