Spread of entanglement and causality
We investigate causality constraints on the time evolution of entanglement entropy after a global quench in relativistic theories. We first provide a general proof that the so-called tsunami velocity is bounded by the speed of light. We then generalize the free particle streaming model of [1] to gen...
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| Format: | Article |
| Language: | English |
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Springer Berlin Heidelberg
2016
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| Online Access: | http://hdl.handle.net/1721.1/103888 https://orcid.org/0000-0002-4911-3183 |
| _version_ | 1826192722561597440 |
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| author | Casini, Horacio Liu, Hong Mezei, Márk |
| author2 | Massachusetts Institute of Technology. Center for Theoretical Physics |
| author_facet | Massachusetts Institute of Technology. Center for Theoretical Physics Casini, Horacio Liu, Hong Mezei, Márk |
| author_sort | Casini, Horacio |
| collection | MIT |
| description | We investigate causality constraints on the time evolution of entanglement entropy after a global quench in relativistic theories. We first provide a general proof that the so-called tsunami velocity is bounded by the speed of light. We then generalize the free particle streaming model of [1] to general dimensions and to an arbitrary entanglement pattern of the initial state. In more than two spacetime dimensions the spread of entanglement in these models is highly sensitive to the initial entanglement pattern, but we are able to prove an upper bound on the normalized rate of growth of entanglement entropy, and hence the tsunami velocity. The bound is smaller than what one gets for quenches in holographic theories, which highlights the importance of interactions in the spread of entanglement in many-body systems. We propose an interacting model which we believe provides an upper bound on the spread of entanglement for interacting relativistic theories. In two spacetime dimensions with multiple intervals, this model and its variations are able to reproduce intricate results exhibited by holographic theories for a significant part of the parameter space. For higher dimensions, the model bounds the tsunami velocity at the speed of light. Finally, we construct a geometric model for entanglement propagation based on a tensor network construction for global quenches. |
| first_indexed | 2024-09-23T09:28:14Z |
| format | Article |
| id | mit-1721.1/103888 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T09:28:14Z |
| publishDate | 2016 |
| publisher | Springer Berlin Heidelberg |
| record_format | dspace |
| spelling | mit-1721.1/1038882022-09-30T14:37:18Z Spread of entanglement and causality Casini, Horacio Liu, Hong Mezei, Márk Massachusetts Institute of Technology. Center for Theoretical Physics Massachusetts Institute of Technology. Department of Physics Liu, Hong We investigate causality constraints on the time evolution of entanglement entropy after a global quench in relativistic theories. We first provide a general proof that the so-called tsunami velocity is bounded by the speed of light. We then generalize the free particle streaming model of [1] to general dimensions and to an arbitrary entanglement pattern of the initial state. In more than two spacetime dimensions the spread of entanglement in these models is highly sensitive to the initial entanglement pattern, but we are able to prove an upper bound on the normalized rate of growth of entanglement entropy, and hence the tsunami velocity. The bound is smaller than what one gets for quenches in holographic theories, which highlights the importance of interactions in the spread of entanglement in many-body systems. We propose an interacting model which we believe provides an upper bound on the spread of entanglement for interacting relativistic theories. In two spacetime dimensions with multiple intervals, this model and its variations are able to reproduce intricate results exhibited by holographic theories for a significant part of the parameter space. For higher dimensions, the model bounds the tsunami velocity at the speed of light. Finally, we construct a geometric model for entanglement propagation based on a tensor network construction for global quenches. United States. Dept. of Energy (cooperative research agreement DE-FG0205ER41360) Princeton Center for Theoretical Science 2016-08-10T20:57:21Z 2016-08-10T20:57:21Z 2016-07 2016-05 2016-08-03T08:09:19Z Article http://purl.org/eprint/type/JournalArticle 1029-8479 http://hdl.handle.net/1721.1/103888 Casini, Horacio, Hong Liu, and Mark Mezei. "Spread of entanglement and causality." Journal of High Energy Physics 2016:77 (July 2016). pp.1-61. https://orcid.org/0000-0002-4911-3183 en http://dx.doi.org/10.1007/JHEP07(2016)077 Journal of High Energy Physics Creative Commons Attribution http://creativecommons.org/licenses/by/4.0/ The Author(s) application/pdf Springer Berlin Heidelberg Springer Berlin Heidelberg |
| spellingShingle | Casini, Horacio Liu, Hong Mezei, Márk Spread of entanglement and causality |
| title | Spread of entanglement and causality |
| title_full | Spread of entanglement and causality |
| title_fullStr | Spread of entanglement and causality |
| title_full_unstemmed | Spread of entanglement and causality |
| title_short | Spread of entanglement and causality |
| title_sort | spread of entanglement and causality |
| url | http://hdl.handle.net/1721.1/103888 https://orcid.org/0000-0002-4911-3183 |
| work_keys_str_mv | AT casinihoracio spreadofentanglementandcausality AT liuhong spreadofentanglementandcausality AT mezeimark spreadofentanglementandcausality |