Time evolution of entanglement for holographic steady state formation
Abstract Within gauge/gravity duality, we consider the local quench-like time evolution obtained by joining two 1+1-dimensional heat baths at different temperatures at time t = 0. A steady state forms and expands in space. For the 2+1-dimensional gravity dual, we find that the “shockwaves” expanding...
| Main Authors: | , , , , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2017-10-01
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| Series: | Journal of High Energy Physics |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1007/JHEP10(2017)034 |
| _version_ | 1818700244265730048 |
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| author | Johanna Erdmenger Daniel Fernández Mario Flory Eugenio Megías Ann-Kathrin Straub Piotr Witkowski |
| author_facet | Johanna Erdmenger Daniel Fernández Mario Flory Eugenio Megías Ann-Kathrin Straub Piotr Witkowski |
| author_sort | Johanna Erdmenger |
| collection | DOAJ |
| description | Abstract Within gauge/gravity duality, we consider the local quench-like time evolution obtained by joining two 1+1-dimensional heat baths at different temperatures at time t = 0. A steady state forms and expands in space. For the 2+1-dimensional gravity dual, we find that the “shockwaves” expanding the steady-state region are of spacelike nature in the bulk despite being null at the boundary. However, they do not transport information. Moreover, by adapting the time-dependent Hubeny-Rangamani-Takayanagi prescription, we holographically calculate the entanglement entropy and also the mutual information for different entangling regions. For general temperatures, we find that the entanglement entropy increase rate satisfies the same bound as in the ‘entanglement tsunami’ setups. For small temperatures of the two baths, we derive an analytical formula for the time dependence of the entanglement entropy. This replaces the entanglement tsunami-like behaviour seen for high temperatures. Finally, we check that strong subadditivity holds in this time-dependent system, as well as further more general entanglement inequalities for five or more regions recently derived for the static case. |
| first_indexed | 2024-12-17T15:01:52Z |
| format | Article |
| id | doaj.art-a71664edd9984d4296f954fbb00690e5 |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-12-17T15:01:52Z |
| publishDate | 2017-10-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-a71664edd9984d4296f954fbb00690e52022-12-21T21:43:53ZengSpringerOpenJournal of High Energy Physics1029-84792017-10-0120171015810.1007/JHEP10(2017)034Time evolution of entanglement for holographic steady state formationJohanna Erdmenger0Daniel Fernández1Mario Flory2Eugenio Megías3Ann-Kathrin Straub4Piotr Witkowski5Max-Planck-Institut für Physik (Werner-Heisenberg-Institut)Max-Planck-Institut für Physik (Werner-Heisenberg-Institut)Max-Planck-Institut für Physik (Werner-Heisenberg-Institut)Max-Planck-Institut für Physik (Werner-Heisenberg-Institut)Max-Planck-Institut für Physik (Werner-Heisenberg-Institut)Max-Planck-Institut für Physik (Werner-Heisenberg-Institut)Abstract Within gauge/gravity duality, we consider the local quench-like time evolution obtained by joining two 1+1-dimensional heat baths at different temperatures at time t = 0. A steady state forms and expands in space. For the 2+1-dimensional gravity dual, we find that the “shockwaves” expanding the steady-state region are of spacelike nature in the bulk despite being null at the boundary. However, they do not transport information. Moreover, by adapting the time-dependent Hubeny-Rangamani-Takayanagi prescription, we holographically calculate the entanglement entropy and also the mutual information for different entangling regions. For general temperatures, we find that the entanglement entropy increase rate satisfies the same bound as in the ‘entanglement tsunami’ setups. For small temperatures of the two baths, we derive an analytical formula for the time dependence of the entanglement entropy. This replaces the entanglement tsunami-like behaviour seen for high temperatures. Finally, we check that strong subadditivity holds in this time-dependent system, as well as further more general entanglement inequalities for five or more regions recently derived for the static case.http://link.springer.com/article/10.1007/JHEP10(2017)034AdS-CFT CorrespondenceGauge-gravity correspondenceHolography and condensed matter physics (AdS/CMT) |
| spellingShingle | Johanna Erdmenger Daniel Fernández Mario Flory Eugenio Megías Ann-Kathrin Straub Piotr Witkowski Time evolution of entanglement for holographic steady state formation Journal of High Energy Physics AdS-CFT Correspondence Gauge-gravity correspondence Holography and condensed matter physics (AdS/CMT) |
| title | Time evolution of entanglement for holographic steady state formation |
| title_full | Time evolution of entanglement for holographic steady state formation |
| title_fullStr | Time evolution of entanglement for holographic steady state formation |
| title_full_unstemmed | Time evolution of entanglement for holographic steady state formation |
| title_short | Time evolution of entanglement for holographic steady state formation |
| title_sort | time evolution of entanglement for holographic steady state formation |
| topic | AdS-CFT Correspondence Gauge-gravity correspondence Holography and condensed matter physics (AdS/CMT) |
| url | http://link.springer.com/article/10.1007/JHEP10(2017)034 |
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