Sachdev-Ye-Kitaev Model
Out-of-Time-Order Correlator (OTOC) & Quantum Chaos
The SYK model is a solvable model of quantum chaos: N Majorana fermions with all-to-all random q=4 interactions J_{ijkl}. The OTOC F(t)=⟨W(t)V(0)W(t)V(0)⟩ probes operator scrambling. For SYK it grows as F(t) ~ 1 − (const/N)e^{λ_L t}, where the Lyapunov exponent λ_L = 2π/β saturates the Maldacena-Shenker-Stanford bound — making SYK a fast scrambler and holographic dual to JT gravity.