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Journal Article

Scrambling is Necessary but Not Sufficient for Chaos

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Kos,  Pavel
Theory, Max Planck Institute of Quantum Optics, Max Planck Society;
MCQST - Munich Center for Quantum Science and Technology, External Organizations;

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2304.07319.pdf
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Citation

Dowling, N., Kos, P., & Modi, K. (2023). Scrambling is Necessary but Not Sufficient for Chaos. Physical Review Letters, 131: 180403. doi:10.1103/PhysRevLett.131.180403.


Cite as: https://hdl.handle.net/21.11116/0000-000D-3C2D-F
Abstract
We show that out-of-time-order correlators (OTOCs) constitute a probe for
Local-Operator Entanglement (LOE). There is strong evidence that a volumetric
growth of LOE is a faithful dynamical signature of quantum chaos, while OTOC
decay corresponds to operator scrambling, often conflated with chaos. We show
that rapid OTOC decay is a necessary but not sufficient condition for linear
(chaotic) growth of the LOE entropy. We analytically support our results
through wide classes of local-circuit models of many-body dynamics, including
both integrable and non-integrable dual-unitary circuits. We show sufficient
conditions under which local dynamics leads to an equivalence of scrambling and
chaos.