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PreprintCC BY 4.0arXiv

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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Cite

BibTeXRIS
BibTeX
@misc{cai2026fast,
  title = {{Fast mixing of the SYK model at high temperatures}},
  author = {Yiyi Cai and Yongtao Zhan and Alexander Zlokapa},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.05953},
  eprint = {2610.05953},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.05953},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Fast mixing of the SYK model at high temperatures
AU  - Yiyi Cai
AU  - Yongtao Zhan
AU  - Alexander Zlokapa
PY  - 2026
DA  - 2026/10/05
PB  - arXiv
DO  - 10.48550/arxiv.2610.05953
UR  - https://arxiv.org/abs/2610.05953
AB  - 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.
ER  -