Randomly Pruning the Sachdev-Ye-Kitaev model

Abstract: 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, we demonstrate 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 $O(L^4)$ couplings in the fully connected SYK model, specifically $O(KL)$, is retained. Here, $L$ represents the number of sites, and $K\sim 10$. 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.