Fast mixing of the SYK model at high temperatures

2026-10-05

AI Summary

This study addresses the significant challenges in analyzing the dynamics and preparing thermal states of the Sachdev-Ye-Kitaev (SYK) model, which arise from its all-to-all disordered interactions. To overcome these difficulties, this work proposes a pseudo-Lindbladian framework for fermionic systems combined with classical dynamical comparison techniques. By transcending the limitations of local correlations, the approach establishes rigorous convergence guarantees under an arbitrary inverse-polynomial trace distance. Furthermore, it proves the existence of a quantum Gibbs sampler exhibiting a system-size-independent spectral gap at high temperatures. The primary contribution of this research is achieving rigorously efficient polynomial-time preparation of SYK Gibbs states on quantum computers, thereby providing both a theoretical foundation and algorithmic support for simulating thermal states of strongly correlated quantum systems.

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.

Problem

• SYK model
• quantum Gibbs sampler
• spectral gap
• fast mixing
• Gibbs state preparation

Innovation

• SYK model
• quantum Gibbs sampler
• pseudo-Lindbladian approach
• spectral gap
• fermionic systems