Fast mixing of the SYK model at high temperatures

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.

Quantum Physics (quant-ph); Disordered Systems and Neural Networks (cond-mat.dis-nn); Data Structures and Algorithms (cs.DS); Mathematical Physics (math-ph)

arXiv:2610.05953 [quant-ph]

(or arXiv:2610.05953v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2610.05953 arXiv-issued DOI via DataCite (pending registration)