Space-time in the SYK model

Das, Sumit R.; Ghosh, Animik; Jevicki, Antal; Suzuki, Kenta

doi:10.1007/jhep07(2018)184

Cited by 68 publications

(58 citation statements)

References 110 publications

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“…This corresponds to a single diffusive peak for the dynamical structure factor S nn (p, ω) at ω ∼ 0. For intermediate value of t/J and t/V , there should be a crossover between (22) and (23). Interestingly, similar crossover also appears in a superfluid when tuning temperature where the second sound connects to a diffusive mode for entropy.…”

Section: Crossover From Dispersive Metal To Diffusive Metal: Chamentioning

confidence: 99%

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Dispersive Sachdev-Ye-Kitaev model: Band structure and quantum chaos

Zhang

2017

Phys. Rev. B

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The Sachdev-Ye-Kitaev (SYK) model is a concrete model for non-Fermi Liquid with maximally chaotic behavior in 0 + 1-d. In order to gain some insights into real materials in higher dimensions where fermions could hop between different sites, here we consider coupling a SYK lattice by a constant hopping. We call this dispersive SYK model. Focusing on 1 + 1-d homogeneous hopping, by either tuning temperature or the relative strength of random interaction (hopping) and constant hopping, we find a crossover between a dispersive metal to an incoherent metal, where dynamic exponent z changes from 1 to ∞. We study the crossover by calculating spectral function, charge density correlator and the Lyapunov exponent. We further find the Lyapunov exponent becomes larger when the chemical potential is tuned to approach a Van Hove singularity because of the large density of states near the Fermi suface. The effect of the topological non-trivial bands is also discussed.

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Section: Crossover From Dispersive Metal To Diffusive Metal: Chamentioning

confidence: 99%

“…The model is studied extensively on both field theory side 1,3-13 and gravity side 3,[14][15][16][17][18][19][20][21][22][23][24][25] . In this paper, we will focus on the the field theory description and the Lagrangian in imaginary time is given by:…”

Section: Introductionmentioning

confidence: 99%

Dispersive Sachdev-Ye-Kitaev model: Band structure and quantum chaos

Zhang

2017

Phys. Rev. B

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“…Recently, different extensions of the SYK model have been studied including several fermionic flavors [42,43], higher dimensions [44][45][46][47][48], one plus two-body interactions [49][50][51], with supersymmetry [52][53][54][55][56][57][58][59] and with no disorder [37,60,61].…”

Section: Introductionmentioning

confidence: 99%

Universality and Thouless energy in the supersymmetric Sachdev-Ye-Kitaev model

2018

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We investigate the supersymmetric Sachdev-Ye-Kitaev (SYK) model, N Majorana fermions with infinite range interactions in 0 þ 1 dimensions. We have found that, close to the ground state E ≈ 0, discrete symmetries alter qualitatively the spectral properties with respect to the non-supersymmetric SYK model. The average spectral density at finite N, which we compute analytically and numerically, grows exponentially with N for E ≈ 0. However the chiral condensate, which is normalized with respect the total number of eigenvalues, vanishes in the thermodynamic limit. Slightly above E ≈ 0, the spectral density grows exponentially with the energy. Deep in the quantum regime, corresponding to the first OðNÞ eigenvalues, the average spectral density is universal and well described by random matrix ensembles with chiral and superconducting discrete symmetries. The dynamics for E ≈ 0 is investigated by level fluctuations. Also in this case we find excellent agreement with the prediction of chiral and superconducting random matrix ensembles for eigenvalue separations smaller than the Thouless energy, which seems to scale linearly with N. Deviations beyond the Thouless energy, which describes how ergodicity is approached, are universally characterized by a quadratic growth of the number variance. In the time domain, we have found analytically that the spectral form factor gðtÞ, obtained from the connected twolevel correlation function of the unfolded spectrum, decays as 1=t 2 for times shorter but comparable to the Thouless time with gð0Þ related to the coefficient of the quadratic growth of the number variance. Our results provide further support that quantum black holes are ergodic and therefore can be classified by random matrix theory.

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“…• The bulk field we defined in (2.34) clearly satisfies the equation of motion of a massive higher spin field in the Euclidean AdS space. When J = 0 and ∆ 1 = ∆ 2 = 0 (2.33) can be seen as the Radon transform that intertwines between the bulk scalar equation of motion and the Casimir equation of the scalar OPE block [58] (see also [73,74] A useful identity Here we will derive the following identity which is used for deriving the momentum space representation of the three-point function:…”

Section: Discussionmentioning

confidence: 99%

The gravity dual of Lorentzian OPE blocks

Chen

Kobayashi

et al. 2020

J. High Energ. Phys.

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We consider the operator product expansion (OPE) structure of scalar primary operators in a generic Lorentzian CFT and its dual description in a gravitational theory with one extra dimension. The OPE can be decomposed into certain bi-local operators transforming as the irreducible representations under conformal group, called the OPE blocks. We show the OPE block is given by integrating a higher spin field along a geodesic in the Lorentzian AdS space-time when the two operators are space-like separated. When the two operators are time-like separated however, we find the OPE block has a peculiar representation where the dual gravitational theory is not defined on the AdS space-time but on a hyperboloid with an additional time coordinate and Minkowski space-time on its boundary. This differs from the surface Witten diagram proposal for the time-like OPE block, but in two dimensions we reproduce it consistently using a kinematical duality between a pair of time-like separated points and space-like ones.

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Space-time in the SYK model

Cited by 68 publications

References 110 publications

Dispersive Sachdev-Ye-Kitaev model: Band structure and quantum chaos

Dispersive Sachdev-Ye-Kitaev model: Band structure and quantum chaos

Universality and Thouless energy in the supersymmetric Sachdev-Ye-Kitaev model

The gravity dual of Lorentzian OPE blocks

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