Scrambling Is Necessary but Not Sufficient for Chaos
Neil Dowling, Pavel Kos, Kavan Modi
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 indicator 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 nonintegrable dual-unitary circuits. We show sufficient conditions under which local dynamics leads to an equivalence of scrambling and chaos.
Topics & Concepts
ScramblingQuantum chaosChaoticQuantum entanglementPhysicsStatistical physicsUnitary stateOperator (biology)Entropy (arrow of time)QuantumQuantum mechanicsMathematicsQuantum dynamicsComputer scienceAlgorithmPolitical scienceGeneChemistryBiochemistryTranscription factorRepressorLawArtificial intelligenceQuantum many-body systemsNeural Networks and Reservoir ComputingQuantum and electron transport phenomena