Void formation in operator growth, entanglement, and unitarity
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13130_2021_Article_15116.pdf
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1.11 MB
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Checksum (MD5)
dc979ed45857ac7f8520abf29ada045e
Author(s)
Liu, Hong
Vardhan, Shreya
Date Issued
March 16, 2021
Publisher
Springer Berlin Heidelberg
Citation
Journal of High Energy Physics. 2021 Mar 16;2021(3):159
Version
Final published version
Abstract
Abstract
The structure of the Heisenberg evolution of operators plays a key role in explaining diverse processes in quantum many-body systems. In this paper, we discuss a new universal feature of operator evolution: an operator can develop a void during its evolution, where its nontrivial parts become separated by a region of identity operators. Such processes are present in both integrable and chaotic systems, and are required by unitarity. We show that void formation has important implications for unitarity of entanglement growth and generation of mutual information and multipartite entanglement. We study explicitly the probability distributions of void formation in a number of unitary circuit models, and conjecture that in a quantum chaotic system the distribution is given by the one we find in random unitary circuits, which we refer to as the random void distribution. We also show that random unitary circuits lead to the same pattern of entanglement growth for multiple intervals as in (1 + 1)-dimensional holographic CFTs after a global quench, which can be used to argue that the random void distribution leads to maximal entanglement growth.
MIT Department
Massachusetts Institute of Technology. Center for Theoretical Physics
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Creative Commons Attribution
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1007/JHEP03(2021)159
