Higher Dimensional Generalizations of the SYK Model
TLDR
In this paper, a 1+1 dimensional generalization of the Sachdev-Ye-Kitaev model is discussed, which contains $N$ Majorana fermions at each lattice site with a nearest-neighbour hopping term.Abstract:
We discuss a 1+1 dimensional generalization of the Sachdev-Ye-Kitaev model. The model contains $N$ Majorana fermions at each lattice site with a nearest-neighbour hopping term. The SYK random interaction is restricted to low momentum fermions of definite chirality within each lattice site. This gives rise to an ordinary 1+1 field theory above some energy scale and a low energy SYK-like behavior. We exhibit a class of low-pass filters which give rise to a rich variety of hyperscaling behaviour in the IR. We also discuss another set of generalizations which describes probing an SYK system with an external fermion, together with the new scaling behavior they exhibit in the IR.read more
Citations
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Journal ArticleDOI
Black Holes and Random Matrices
Jordan Cotler,Guy Gur-Ari,Masanori Hanada,Masanori Hanada,Masanori Hanada,Joseph Polchinski,Joseph Polchinski,Phil Saad,Stephen H. Shenker,Douglas Stanford,Alexandre Streicher,Alexandre Streicher,Masaki Tezuka +12 more
TL;DR: In this paper, the authors show that the late time behavior of horizon fluctuations in large anti-de Sitter (AdS) black holes is governed by the random matrix dynamics characteristic of quantum chaotic systems.
Posted Content
An SYK-Like Model Without Disorder
TL;DR: In this paper, it was shown that it is possible to construct a quantum system without quenched disorder that has the same large $n$ limit for its correlation functions and thermodynamics as the SYK model.
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Solvable model for a dynamical quantum phase transition from fast to slow scrambling
TL;DR: In this article, an extension of the SYK model was proposed, which exhibits a quantum phase transition from the previously identified non-Fermi liquid fixed point to a Fermi-liquid-like state, while still allowing an exact solution in a suitable large-$N$ limit.
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More on supersymmetric and 2d analogs of the SYK model
TL;DR: In this paper, supersymmetric and 2D analogies of the SYK model were explored and an integral formula for the four-point function at order 1/N was derived for the chaos exponent and some anomalous dimensions.
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Power-law out of time order correlation functions in the SYK model
TL;DR: In this article, the authors evaluate the finite temperature partition sum and correlation functions of the SYK model and show that at time scales proportional to the number of particles, the out-of-time order correlation function crosses over from a regime of exponential decay to a universal t−6 power-law behavior.
References
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A bound on chaos
TL;DR: In this paper, a sharp bound on the rate of growth of chaos in thermal quantum systems with a large number of degrees of freedom is given, based on plausible physical assumptions, establishing this conjecture.
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Remarks on the Sachdev-Ye-Kitaev model
Juan Maldacena,Douglas Stanford +1 more
TL;DR: In this paper, the authors studied the quantum mechanical model of $N$ Majorana fermions with random interactions of a few Fermions at a time (Sachdev-Ye-Kitaev model) in the large N$ limit.
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