Spectral form factor in sparse SYK models

Cáceres, Elena; Misobuchi, Anderson Seigo; Raz, Amir

doi:10.1007/jhep08(2022)236

Cited by 10 publications

(9 citation statements)

References 31 publications

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“…) ∼ 2 N∕2 , the number of coupling terms in this model is relatively small. However, as demonstrated in the aforementioned references, [7][8][9][10] even if a number of coupling terms on the order of O(N) are retained, the model continues to exhibit predominantly chaotic behavior. While much of the initial motivation for pruning the SYK model stemmed from simulating SYK on a quantum computer with the hope of gaining insights into properties of quantum gravity models, pruning the SYK also gives rise to broader questions related to deviations from chaotic behavior.…”

Section: N∕4mentioning

confidence: 93%

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Randomly Pruning the Sachdev‐Ye‐Kitaev Model

Berkovits

2024

Adv Quantum Tech

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The Sachdev‐Ye‐Kitaev model (SYK) is renowned for its short‐time chaotic behavior, which plays a fundamental role in its application to various fields such as quantum gravity and holography. The Thouless energy, representing the energy scale at which the universal chaotic behavior in the energy spectrum ceases, can be determined from the spectrum itself. When simulating the SYK model on classical or quantum computers, it is advantageous to minimize the number of terms in the Hamiltonian by randomly pruning the couplings. In this paper, it is demonstrated that even with a significant pruning, eliminating a large number of couplings, the chaotic behavior persists up to short time scales. This is true even when only a fraction of the original couplings in the fully connected SYK model, specifically , is retained. Here, L represents the number of sites, and . The properties of the long‐range energy scales, corresponding to short time scales, are verified through numerical singular value decomposition (SVD) and level number variance calculations.

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Section: N∕4mentioning

confidence: 93%

“…[6] The idea of simplifying the classical computation involved in the SYK model by removing certain coupling terms was proposed in several previous studies. [7][8][9][10] The approach involved pruning the coupling terms either randomly or by ensuring that each site is coupled to a fixed fraction of other sites. In ref.…”

Section: Introductionmentioning

confidence: 99%

Randomly Pruning the Sachdev‐Ye‐Kitaev Model

Berkovits

2024

Adv Quantum Tech

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“…Rigorous proofs of quantum chaos by computing the SFF have been preformed in kicked spin chains [ 17 , 18 ] and more generally in dual-unitary circuits [ 19 , 20 ]. In the high-energy physics context, for example, studies of the SFF have been performed in Sachdev–Ye–Kitaev-type models [ 21 , 22 , 23 , 24 ] and using hydrodynamic theories [ 25 ]. Pioneering experimental studies of the SFF were carried out on excitation spectra of molecules [ 26 ] and microwave billiards [ 27 ].…”

Section: Introductionmentioning

confidence: 99%

Spectral Form Factor and Dynamical Localization

Lozej

2023

Entropy

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Quantum dynamical localization occurs when quantum interference stops the diffusion of wave packets in momentum space. The expectation is that dynamical localization will occur when the typical transport time of the momentum diffusion is greater than the Heisenberg time. The transport time is typically computed from the corresponding classical dynamics. In this paper, we present an alternative approach based purely on the study of spectral fluctuations of the quantum system. The information about the transport times is encoded in the spectral form factor, which is the Fourier transform of the two-point spectral autocorrelation function. We compute large samples of the energy spectra (of the order of 106 levels) and spectral form factors of 22 stadium billiards with parameter values across the transition between the localized and extended eigenstate regimes. The transport time is obtained from the point when the spectral form factor transitions from the non-universal to the universal regime predicted by random matrix theory. We study the dependence of the transport time on the parameter value and show the level repulsion exponents, which are known to be a good measure of dynamical localization, depend linearly on the transport times obtained in this way.

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“…Binary interactions are traditionally used in physics, but higher-order interactions appear, e.g. in recent studies of toy models of quantum chaos [31][32][33][34][35].…”

Section: Introductionmentioning

confidence: 99%

Random recursive hypergraphs

Krapivsky

2023

J. Phys. A: Math. Theor.

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Random recursive hypergraphs grow by adding, at each step, a vertex and an edge formed by joining the new vertex to a randomly chosen existing edge. The model is parameter-free, and several characteristics of emerging hypergraphs admit neat expressions via harmonic numbers, Bernoulli numbers, Eulerian numbers, and Stirling numbers of the first kind. Natural deformations of random recursive hypergraphs give rise to fascinating models of growing random hypergraphs.

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Spectral form factor in sparse SYK models

Cited by 10 publications

References 31 publications

Randomly Pruning the Sachdev‐Ye‐Kitaev Model

Randomly Pruning the Sachdev‐Ye‐Kitaev Model

Spectral Form Factor and Dynamical Localization

Random recursive hypergraphs

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