Sachdev-Ye-Kitaev Model: Quantum Scrambling

Sachdev-Ye-Kitaev (SYK) Model: N Majorana fermions with all-to-all random 4-body interactions J_{ijkl}. The SYK model is a maximally chaotic quantum system and a holographic dual to a 2D black hole (JT gravity).

OTOC: The out-of-time-order correlator C(t) = −⟨[W(t),V(0)]²⟩/⟨W²⟩⟨V²⟩ measures quantum information scrambling. In the SYK model: C(t) ≈ 1 − (1/N)e^{λ_L t} with Lyapunov exponent λ_L = 2π/β, saturating the Maldacena-Shenker-Stanford chaos bound.

Scrambling time: t_* = β/(2π) · ln(N) — logarithmically fast, like black holes.