Fast mixing of the SYK model at high temperatures

Yiyi Cai; Yongtao Zhan; Alexander Zlokapa

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arXiv · 2610.05953

Fast mixing of the SYK model at high temperatures

Yiyi Cai·Yongtao Zhan·Alexander Zlokapa

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Abstract

The Sachdev-Ye-Kitaev (SYK) model is a strongly interacting fermionic system. Its dynamics are difficult to analyze with Lieb-Robinson bounds and cluster expansions due to its all-to-all disordered interactions. We prove that, with high probability over the disorder, the SYK model admits a quantum Gibbs sampler with a system-size-independent spectral gap at sufficiently high constant temperatures. This yields polynomial-time preparation of SYK Gibbs states on a quantum computer. While prior non-rigorous computations that suggested SYK thermalization were limited to studying local correlators, we emphasize that our result holds up to arbitrary inverse polynomial trace distance. Our proof introduces the pseudo-Lindbladian approach to fermions and uses an especially simple SYK analysis based on a comparison to classical dynamics.

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quant-ph cond-mat.dis-nn cs.DS math-ph math.MP

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Yiyi Cai, Yongtao Zhan, Alexander Zlokapa. 2026-10-05. Fast mixing of the SYK model at high temperatures. https://arxiv.org/abs/2610.05953

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