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<p>The Sachdev-Ye-Kitaev (SYK) model is a system of <i>N</i> Majorana fermions with random interactions and strongly chaotic dynamics, which at low energy admits a holographically dual description as two-dimensional Jackiw-Teitelboim gravity. Hence the SYK model provides a toy model of quantum gravity that might be feasible to simulate with near-term quantum hardware. Motivated by the goal of reducing the resources needed for such a simulation, we study a sparsified version of the SYK model, in which interaction terms are deleted with probability 1<i>−p</i>. Specifically, we compute numerically the spectral form factor (SFF, the Fourier transform of the Hamiltonian’s eigenvalue pair correlation function) and the nearest-neighbor eigenvalue gap ratio <i>r</i> (characterizing the distribution of gaps between consecutive eigenvalues). We find that when <i>p</i> is greater than a transition value <i>p</i><sub>1</sub>, which scales as 1/<i>N</i> <sup>3</sup>, both the SFF and <i>r</i> match the values attained by the full unsparsified model and with expectations from random matrix theory (RMT). But for <i>p &lt; p</i><sub>1</sub>, deviations from unsparsified SYK and RMT occur, indicating a breakdown of holography in the highly sparsified regime. Below an even smaller value <i>p</i><sub>2</sub>, which also scales as 1/<i>N</i> <sup>3</sup>, even the spacing of consecutive eigenvalues differs from RMT values, signaling a complete breakdown of spectral rigidity. Our results cast doubt on the holographic interpretation of very highly sparsified SYK models obtained via machine learning using teleportation infidelity as a loss function.</p>

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Quantum chaos in the sparse SYK model

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年2月26日

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  • Patrick Orman,
  • Hrant Gharibyan,
  • John Preskill

摘要

The Sachdev-Ye-Kitaev (SYK) model is a system of N Majorana fermions with random interactions and strongly chaotic dynamics, which at low energy admits a holographically dual description as two-dimensional Jackiw-Teitelboim gravity. Hence the SYK model provides a toy model of quantum gravity that might be feasible to simulate with near-term quantum hardware. Motivated by the goal of reducing the resources needed for such a simulation, we study a sparsified version of the SYK model, in which interaction terms are deleted with probability 1−p. Specifically, we compute numerically the spectral form factor (SFF, the Fourier transform of the Hamiltonian’s eigenvalue pair correlation function) and the nearest-neighbor eigenvalue gap ratio r (characterizing the distribution of gaps between consecutive eigenvalues). We find that when p is greater than a transition value p1, which scales as 1/N 3, both the SFF and r match the values attained by the full unsparsified model and with expectations from random matrix theory (RMT). But for p < p1, deviations from unsparsified SYK and RMT occur, indicating a breakdown of holography in the highly sparsified regime. Below an even smaller value p2, which also scales as 1/N 3, even the spacing of consecutive eigenvalues differs from RMT values, signaling a complete breakdown of spectral rigidity. Our results cast doubt on the holographic interpretation of very highly sparsified SYK models obtained via machine learning using teleportation infidelity as a loss function.