Spread of entanglement and causality
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13130_2016_Article_4334.pdf
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2.94 MB
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Checksum (MD5)
779c8a0d5453a768d016b3a7799199e5
Author(s)
Casini, Horacio
Liu, Hong
Mezei, Márk
Date Issued
July 2016
Journal
Journal of High Energy Physics
Publisher
Springer Berlin Heidelberg
Citation
Casini, Horacio, Hong Liu, and Mark Mezei. "Spread of entanglement and causality." Journal of High Energy Physics 2016:77 (July 2016). pp.1-61.
Version
Final published version
Abstract
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.
MIT Department
Massachusetts Institute of Technology. Center for Theoretical Physics
Massachusetts Institute of Technology. Department of Physics
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Creative Commons Attribution
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DOI of Published Version
http://dx.doi.org/10.1007/JHEP07(2016)077
