← 研踪 PaperTrailarXiv:2610.05953 · v2
Fast mixing of the SYK model at high temperatures
首次提交 2026-10-05 16:06
版本更新 2026-11-03 13:33
雷达观测 2026-11-04 23:40
摘要
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 then applies two key new ideas: a Bochner inequality for quantum dynamics, and an especially simple SYK analysis based on a comparison to classical dynamics.
作者备注：34 pages; v2 improves exposition and updates references
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v2 · 2026-11-03 13:33 · 最新观测版本
Fast mixing of the SYK model at high temperatures
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 then applies two key new ideas: a Bochner inequality for quantum dynamics, and an especially simple SYK analysis based on a comparison to classical dynamics.
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