Correlation measures and the entanglement wedge cross-section after quantum quenches in two-dimensional conformal field theories
Abstract We consider the time evolution of mixed state correlation measures in two-dimensional conformal field theories, such as logarithmic negativity, odd entropy, and reflected entropy, after quantum quenches of various kinds. These correlation measures, in the holographic context, are all associ...
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doaj-54b60b35f1f342a197556097740591cd2020-11-25T02:02:52ZengSpringerOpenJournal of High Energy Physics1029-84792020-04-012020414210.1007/JHEP04(2020)074Correlation measures and the entanglement wedge cross-section after quantum quenches in two-dimensional conformal field theoriesJonah Kudler-Flam0Yuya Kusuki1Shinsei Ryu2Kadanoff Center for Theoretical Physics, University of ChicagoCenter for Gravitational Physics, Yukawa Institute for Theoretical Physics (YITP), Kyoto UniversityKadanoff Center for Theoretical Physics, University of ChicagoAbstract We consider the time evolution of mixed state correlation measures in two-dimensional conformal field theories, such as logarithmic negativity, odd entropy, and reflected entropy, after quantum quenches of various kinds. These correlation measures, in the holographic context, are all associated to the entanglement wedge cross section. We contrast various classes of conformal field theories, both rational and irrational (pure) conformal field theories. First, for rational conformal field theories, whose dynamics can be well described by the quasi-particle picture, we find all four quantities for disjoint intervals to be proportional, regardless of the specific quench protocol. Second, using the light cone boot- strap, we generalize our results to irrational conformal field theories where we find sharp distinctions from the quasi-particle results and striking differences between mutual information and the other measures. The large surplus of logarithmic negativity relative to mutual information forces us to reconsider what mutual information and logarithmic negativity really measure. We interpret these results as a signature of information scrambling and chaos in irrational theories. These CFT results perfectly agree with our gravitational (holographic) calculations. Furthermore, using holography, we are able to generalize the results to outside of the light cone limit. Finally, due to the breakdown of the quasi-particle picture for irrational theories, we appeal to the “line-tension picture,” motivated by random unitary circuits, as a phenomenological description. We observe that random unitary circuits, with local Hilbert space dimension determined by the Cardy formula, have precisely the same entanglement dynamics as irrational (including holographic) conformal field theories.http://link.springer.com/article/10.1007/JHEP04(2020)074AdS-CFT CorrespondenceConformal Field Theory |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Jonah Kudler-Flam Yuya Kusuki Shinsei Ryu |
spellingShingle |
Jonah Kudler-Flam Yuya Kusuki Shinsei Ryu Correlation measures and the entanglement wedge cross-section after quantum quenches in two-dimensional conformal field theories Journal of High Energy Physics AdS-CFT Correspondence Conformal Field Theory |
author_facet |
Jonah Kudler-Flam Yuya Kusuki Shinsei Ryu |
author_sort |
Jonah Kudler-Flam |
title |
Correlation measures and the entanglement wedge cross-section after quantum quenches in two-dimensional conformal field theories |
title_short |
Correlation measures and the entanglement wedge cross-section after quantum quenches in two-dimensional conformal field theories |
title_full |
Correlation measures and the entanglement wedge cross-section after quantum quenches in two-dimensional conformal field theories |
title_fullStr |
Correlation measures and the entanglement wedge cross-section after quantum quenches in two-dimensional conformal field theories |
title_full_unstemmed |
Correlation measures and the entanglement wedge cross-section after quantum quenches in two-dimensional conformal field theories |
title_sort |
correlation measures and the entanglement wedge cross-section after quantum quenches in two-dimensional conformal field theories |
publisher |
SpringerOpen |
series |
Journal of High Energy Physics |
issn |
1029-8479 |
publishDate |
2020-04-01 |
description |
Abstract We consider the time evolution of mixed state correlation measures in two-dimensional conformal field theories, such as logarithmic negativity, odd entropy, and reflected entropy, after quantum quenches of various kinds. These correlation measures, in the holographic context, are all associated to the entanglement wedge cross section. We contrast various classes of conformal field theories, both rational and irrational (pure) conformal field theories. First, for rational conformal field theories, whose dynamics can be well described by the quasi-particle picture, we find all four quantities for disjoint intervals to be proportional, regardless of the specific quench protocol. Second, using the light cone boot- strap, we generalize our results to irrational conformal field theories where we find sharp distinctions from the quasi-particle results and striking differences between mutual information and the other measures. The large surplus of logarithmic negativity relative to mutual information forces us to reconsider what mutual information and logarithmic negativity really measure. We interpret these results as a signature of information scrambling and chaos in irrational theories. These CFT results perfectly agree with our gravitational (holographic) calculations. Furthermore, using holography, we are able to generalize the results to outside of the light cone limit. Finally, due to the breakdown of the quasi-particle picture for irrational theories, we appeal to the “line-tension picture,” motivated by random unitary circuits, as a phenomenological description. We observe that random unitary circuits, with local Hilbert space dimension determined by the Cardy formula, have precisely the same entanglement dynamics as irrational (including holographic) conformal field theories. |
topic |
AdS-CFT Correspondence Conformal Field Theory |
url |
http://link.springer.com/article/10.1007/JHEP04(2020)074 |
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