Quantum chaos in the sparse SYK model

• URL: http://arxiv.org/abs/2403.13884v2
• Date: Sat, 28 Sep 2024 23:15:20 GMT
• Title: Quantum chaos in the sparse SYK model
• Abstract summary: The Sachdev-Ye-Kitaev (SYK) model is a system of $N$ Majorana fermions with random interactions and strongly chaotic dynamics. We study a sparsified version of the SYK model, in which interaction terms are deleted with probability $1-p$.
• Score: 0.6144680854063939
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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 $p_1$, 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 $p<p_1$, deviations from unsparsified SYK and RMT occur, indicating a breakdown of holography in the highly sparsified regime. Below an even smaller value $p_2$, 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.

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