2018
DOI: 10.1103/physrevx.8.021013
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Operator Hydrodynamics, OTOCs, and Entanglement Growth in Systems without Conservation Laws

Abstract: Thermalization and scrambling are the subject of much recent study from the perspective of manybody quantum systems with locally bounded Hilbert spaces ("spin chains"), quantum field theory and holography. We tackle this problem in 1D spin-chains evolving under random local unitary circuits and prove a number of exact results on the behavior of out-of-time-ordered commutators (OTOCs), and entanglement growth in this setting. These results follow from the observation that the spreading of operators in random ci… Show more

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Cited by 664 publications
(817 citation statements)
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“…As expected, we see from Fig. 6(a) a separation of time scales for the initial state (38). In order to make this more transparent, and following the previous section, we report in Fig.…”
Section: B Random Dynamics With a Conserved U (1) Chargesupporting
confidence: 77%
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“…As expected, we see from Fig. 6(a) a separation of time scales for the initial state (38). In order to make this more transparent, and following the previous section, we report in Fig.…”
Section: B Random Dynamics With a Conserved U (1) Chargesupporting
confidence: 77%
“…However, for large N one expects the effect of fluctuations in the disorder to be small, so that the behavior of S K (t) should be qualitatively the same as the averaged Rényi-2 entropy [38].…”
Section: The Entanglement Growthmentioning
confidence: 99%
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“…Perhaps the physics of scrambling resilience can be related to known types of robustness, e.g., the robustness of renormalization-group fixed points. It would be interesting to probe resilience in many other recently studied models, including noninteracting, weakly coupled, and semiclassical systems [15,[48][49][50][51][52], many-body-localized states [53][54][55][56][57], the SYK model [6,[43][44][45], open systems [37], local random-circuit models [58][59][60][61], other special solvable models [28], and much else.…”
Section: Discussionmentioning
confidence: 99%