Spread of entanglement in a Sachdev-Ye-Kitaev chain

Gu, Yingfei; Lucas, Andrew; Qi, Xiao-Liang

doi:10.1007/jhep09(2017)120

Cited by 110 publications

(183 citation statements)

References 76 publications

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“…(8) and (20), this class of functions is sufficiently broad to suggest that even more general long-range correlations decaying slower than a certain critical power-law (evaluated above as (d + 2)/2) could give rise to the behavior that is markedly different from that obtained in the generic short-range correlated 'SYK-lattice' models, including those with the 'same and nearest neighbor only' [13,42] as well as exponentially decaying random couplings.…”

Section: Fluctuations About Mean-field Solutionsmentioning

confidence: 88%

“…[13,42] where the function J (11) below) pertaining to the above two cases appear to be exactly identical, the only difference stemming from the additional 'Hartree-type' (or 'tadpole') terms which are present in the latter -but not the former -case.…”

Section: (Non-)local Disorder Correlationsmentioning

confidence: 97%

“…[37][38][39][40][41][42][43][44][45][46][47][48][49][50][51][52][53][54] involves a single copy of the SYK 'impurity' coupled to a 1d chain of ordinary fermions and pairwise random couplings between the chain and the SYK fermions. Also, a supersymmetric generalization of the SYK model whose spectrum contains two-fermion bound states, alongside the fundamental fermions, was proposed in Ref.…”

Section: Generalized Syk-like Modelsmentioning

confidence: 99%

“…Focusing on the component T ττ which represents energy density, in the short-range-correlated SYK-chain model of Refs. [13,42] one obtains…”

Section: Diffusive Transport and Chaotic Propertiesmentioning

confidence: 99%

“…In Refs. [13,39,41,42,46] the expression (49) would be further forced into the conventional diffusion propagator by subtracting its value at k = 0 and discarding the term ∼ ω 3 in the numerator.…”

Section: Diffusive Transport and Chaotic Propertiesmentioning

confidence: 99%

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Thickening and sickening the SYK model

Khveshchenko

2018

SciPost Phys.

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We discuss higher dimensional generalizations of the 0 + 1-dimensional Sachdev-YeKitaev (SYK) model that has recently become the focus of intensive interdisciplinary studies by, both, the condensed matter and field-theoretical communities. Unlike the previous constructions where multiple SYK copies would be coupled to each other and/or hybridized with itinerant fermions via spatially short-ranged random hopping processes, we study algebraically varying long-range (spatially and/or temporally) correlated random couplings in the general d + 1 dimensions. Such pertinent topics as translationallyinvariant strong-coupling solutions, emergent reparametrization symmetry, effective action for fluctuations, chaotic behavior, and diffusive transport (or a lack thereof) are all addressed. We find that the most appealing properties of the original SYK model that suggest the existence of its 1+1-dimensional holographic gravity dual do not survive the aforementioned generalizations, thus lending no additional support to the hypothetical broad (including 'non-AdS d+2 /non-C F T d+1 ') holographic correspondence.

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Section: Fluctuations About Mean-field Solutionsmentioning

confidence: 88%

Section: (Non-)local Disorder Correlationsmentioning

confidence: 97%

Section: Generalized Syk-like Modelsmentioning

confidence: 99%

“…Focusing on the component T ττ which represents energy density, in the short-range-correlated SYK-chain model of Refs. [13,42] one obtains…”

Section: Diffusive Transport and Chaotic Propertiesmentioning

confidence: 99%

Section: Diffusive Transport and Chaotic Propertiesmentioning

confidence: 99%

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Thickening and sickening the SYK model

Khveshchenko

2018

SciPost Phys.

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Chaos-protected locality

Jian

Swingle

2022

J. High Energ. Phys.

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Microscopic speed limits that constrain the motion of matter, energy, and information abound in physics, from the “ultimate” speed limit set by light to Lieb-Robinson speed limits in quantum spin systems. In addition to these state-independent speed limits, systems can also be governed by emergent state-dependent speed limits indicating slow dynamics arising, for example, from slow low-energy quasiparticles. Here we describe a different kind of speed limit: a situation where complex information/entanglement spreads rapidly, in a fashion inconsistent with any speed limit, but where simple signals continue to obey an approximate speed limit. If we take the point of view that the motion of simple signals defines the local spacetime geometry of the universe, then the effects we describe show that spacetime locality can be compatible with a high degree of non-local interactions provided these are sufficiently chaotic. With this perspective, we sharpen a puzzle about black holes recently raised by Shor and propose a schematic resolution.

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Frame potential of Brownian SYK model of Majorana and Dirac fermions

Tiutiakina,

De Luca,

De Nardis

2024

J. High Energ. Phys.

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We consider the Brownian SYK, i.e. a system of N Majorana (Dirac) fermions with a white-noise q-body interaction term. We focus on the dynamics of the Frame potentials, a measure of the scrambling and chaos, given by the moments of the overlap between two independent realisations of the model. By means of a Keldysh path-integral formalism, we compute its early and late-time value. We show that, for q > 2, the late time path integral saddle point correctly reproduces the saturation to the value of the Haar frame potential. On the contrary, for q = 2, the model is quadratic and consistently we observe saturation to the Haar value in the restricted space of Gaussian states (Gaussian Haar). The latter is characterised by larger system size corrections that we correctly capture by counting the Goldstone modes of the Keldysh saddle point. Finally, in the case of Dirac fermions, we highlight and resolve the role of the global U(1) symmetry.

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Spread of entanglement in a Sachdev-Ye-Kitaev chain

Cited by 110 publications

References 76 publications

Thickening and sickening the SYK model

Thickening and sickening the SYK model

Chaos-protected locality

Frame potential of Brownian SYK model of Majorana and Dirac fermions

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