Onset of many-body chaos in the 
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Chowdhury, Debanjan; Swingle, Brian

doi:10.1103/physrevd.96.065005

Cited by 130 publications

(191 citation statements)

References 70 publications

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“…OTOCs were computed in thermal weakly coupled systems by summing classes of Feynman diagrams [12][13][14][15]. 6 Our bound (1.8) applies to these results, and it would be interesting to extract the VDLE from the formulas in the literature.…”

Section: Introduction and Summary Of Resultsmentioning

confidence: 99%

Chaos in the butterfly cone

Mezei

Sárosi

2020

J. High Energ. Phys.

146

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A simple probe of chaos and operator growth in many-body quantum systems is the out of time ordered four point function. In a large class of local systems, the effects of chaos in this correlator build up exponentially fast inside the so called butterfly cone. It has been previously observed that the growth of these effects is organized along rays and can be characterized by a velocity dependent Lyapunov exponent, λ(v). We show that this exponent is bounded inside the butterfly cone as λ(v) ≤ 2πT (1 − |v|/v B ), where T is the temperature and v B is the butterfly speed. This result generalizes the chaos bound of Maldacena, Shenker and Stanford. We study λ(v) in some examples such as two dimensional SYK models and holographic gauge theories, and observe that in these systems the bound gets saturated at some critical velocity v * < v B . In this sense, boosting a system enhances chaos. We discuss the connection to conformal Regge theory, where λ(v) is related to the spin of the leading large N Regge trajectory, and controls the four point function in an interpolating regime between the Regge and the light cone limit. Finally, we comment on the generalization of the chaos bound to boosted and rotating ensembles and clarify some recent results on this in the literature.

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Section: Introduction and Summary Of Resultsmentioning

confidence: 99%

Chaos in the butterfly cone

Mezei

Sárosi

2020

J. High Energ. Phys.

146

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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%

Resilience of scrambling measurements

Swingle

Halpern

2018

Phys. Rev. A

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Most experimental protocols for measuring scrambling require time evolution with a Hamiltonian and with the Hamiltonian's negative counterpart (backward time evolution). Engineering controllable quantum many-body systems for which such forward and backward evolution is possible is a significant experimental challenge. Furthermore, if the system of interest is quantum chaotic, one might worry that any small errors in the time reversal will be rapidly amplified, obscuring the physics of scrambling. This paper undermines this expectation: We exhibit a renormalization protocol that extracts nearly ideal out-of-time-ordered-correlator measurements from imperfect experimental measurements. We analytically and numerically demonstrate the protocol's effectiveness, up to the scrambling time, in a variety of models and for sizable imperfections. The scheme extends to errors from decoherence by an environment.

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“…Of course, the model is also of great interest in condensed matter physics [51,54,[57][58][59][60][61][62][63][64][65][66][67]. Other related recent work can be found in [68][69][70][71][72][73][74][75][76][77][78][79][80][81][82][83].…”

Section: Introductionmentioning

confidence: 99%

Correlators in the N = 2 $$ \mathcal{N}=2 $$ supersymmetric SYK model

Peng

Spradlin

Volovich

2017

J. High Energ. Phys.

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We study correlation functions in the one-dimensional N = 2 supersymmetric SYK model. The leading order 4-point correlation functions are computed by summing over ladder diagrams expanded in a suitable basis of conformal eigenfunctions. A novelty of the N = 2 model is that both symmetric and antisymmetric eigenfunctions are required. Although we use a component formalism, we verify that the operator spectrum and 4-point functions are consistent with N = 2 supersymmetry. We also confirm the maximally chaotic behavior of this model and comment briefly on its 6-point functions.

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Onset of many-body chaos in the O(N) model

Cited by 130 publications

References 70 publications

Chaos in the butterfly cone

Chaos in the butterfly cone

Resilience of scrambling measurements

Correlators in the N = 2 $$ \mathcal{N}=2 $$ supersymmetric SYK model

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