The Thouless time for mass-deformed SYK

Nosaka, Tomoki; Rosa, Dario; Yoon, Junggi

doi:10.1007/jhep09(2018)041

Cited by 59 publications

(50 citation statements)

References 135 publications

(237 reference statements)

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“…One may investigate deformed models, such as eg. SYK 4 + SYK 2 [38,39]. Our preliminary investigation [69] points to similarities between level and eigenfunction statistics of such models to those of random regular graphs (RRG) [70][71][72][73][74].…”

Section: Discussionmentioning

confidence: 99%

“…It also turned out to be a convenient tool to investigate thermalization and chaos [4,[12][13][14][15][16][17][18][19][20][21] in the many-body framework. A number of applications towards condensed matter physics [22][23][24][25][26][27][28][29] as well as certain interesting generalizations [27,[30][31][32][33][34][35][36][37][38][39] were proposed. By now there is a firm understanding of its manybody density of states [40][41][42], level-statistics [13,15], and certain correlation functions [14,[43][44][45][46][47][48][49].…”

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confidence: 99%

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On the replica structure of Sachdev-Ye-Kitaev model

Wang

Bagrets

Chudnovskiy

et al. 2019

J. High Energ. Phys.

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We investigate existence of replica off-diagonal solutions in the field-theoretical description of Sachdev-Ye-Kitaev model. To this end we evaluate a set of local and non-local dynamic correlation functions in the long time limit. We argue that the structure of the softmode Schwarzian action is qualitatively different in replica-diagonal vs. replica-off-diagonal scenarios, leading to distinct long-time predictions for the correlation functions. We then evaluate the corresponding correlation functions numerically and compare the simulations with analytical predictions of replica-diagonal and replica-off-diagonal calculations. We conclude that all our numerical results are in a quantitative agreement with the theory based on the replica-diagonal saddle point plus Schwarzian and massive Gaussian fluctuations (the latter do contain replica off-diagonal components). This seems to exclude any contributions from replica-off-diagonal saddle points, at least on the time scales shorter than the inverse many-body level spacing.

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Section: Discussionmentioning

confidence: 99%

mentioning

confidence: 99%

On the replica structure of Sachdev-Ye-Kitaev model

Wang

Bagrets

Chudnovskiy

et al. 2019

J. High Energ. Phys.

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“…This motivate us to expect that the return amplitude in more generic quantum systems like chaotic CFTs shows these structure after the time average. We also compare the shifted spectral form factor (35) where the ensemble average of the spectral form factor is replaced by the time average. As we pointed out, their late time value is not exactly the same, but the behavior shows good agreement on each time.…”

Section: E Time Average Of Single Sample In the Syk Modelmentioning

confidence: 99%

Late time quantum chaos of pure states in random matrices and in the Sachdev-Ye-Kitaev model

Numasawa

2019

Phys. Rev. D

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In this letter, we study the return amplitude, which is the overlap between the initial state and the time evolved state, in the Sachdev-Ye-Kitaev (SYK) model. Initial states are taken to be product states in a spin basis. We numerically study the return amplitude by exactly diagonalizing the Hamiltonian. We also derive the analytic expression for the return amplitude in random matrix theory. The SYK results agree with the random matrix expectation. We also study the time evolution under the different Hamiltonian that describes the traversable wormholes in projected black holes in the context of holography. The time evolution now depends on the choice of initial product states. The results are again explained by random matrix theory. In the symplectic ensemble cases, we observed an interesting pattern of the return amplitude where they show the second dip, ramp and plateau like behavior.

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“…The correlation hole has been studied in full random matrices [29], in many-body systems with [21,[30][31][32][33] and without disorder [31], in the Sachdev-Ye-Kitaev model [34][35][36], which is a two-body random ensemble [37], and in the finite one-dimensional Anderson model [38]. The hole is not exclusive to the survival probability, but emerges also in experimental local observables [32,33].…”

Section: Introductionmentioning

confidence: 99%

Dynamical signatures of quantum chaos and relaxation time scales in a spin-boson system

et al. 2019

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Quantum systems whose classical counterparts are chaotic typically have highly correlated eigenvalues and level statistics that coincide with those from ensembles of full random matrices. A dynamical manifestation of these correlations comes in the form of the so-called correlation hole, which is a dip below the saturation point of the survival probability's time evolution. In this work, we study the correlation hole in the spin-boson (Dicke) model, which presents a chaotic regime and can be realized in experiments with ultracold atoms and ion traps. We derive an analytical expression that describes the entire evolution of the survival probability and allows us to determine the timescales of its relaxation to equilibrium. This expression shows remarkable agreement with our numerical results. While the initial decay and the time to reach the minimum of the correlation hole depend on the initial state, the dynamics beyond the hole up to equilibration is universal. We find that the relaxation time of the survival probability for the Dicke model increases linearly with system size. arXiv:1905.03253v2 [cond-mat.stat-mech]

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The Thouless time for mass-deformed SYK

Cited by 59 publications

References 135 publications

On the replica structure of Sachdev-Ye-Kitaev model

On the replica structure of Sachdev-Ye-Kitaev model

Late time quantum chaos of pure states in random matrices and in the Sachdev-Ye-Kitaev model

Dynamical signatures of quantum chaos and relaxation time scales in a spin-boson system

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