Randomly Pruning the Sachdev-Ye-Kitaev model
- URL: http://arxiv.org/abs/2401.07325v1
- Date: Sun, 14 Jan 2024 16:20:16 GMT
- Title: Randomly Pruning the Sachdev-Ye-Kitaev model
- Authors: Richard Berkovits
- Abstract summary: The Sachdev-Ye-Kitaev model (SYK) is renowned for its short-time chaotic behavior.
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.
- Score: 0.0
- License: http://creativecommons.org/licenses/by-nc-nd/4.0/
- 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.
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