Analytic proof of optimal scrambling in the chiral spin-chain

Prove analytically that the spin-1/2 chiral spin-chain with nearest-neighbor XY coupling of strength u and a three-spin scalar chirality interaction S_n · (S_{n+1} × S_{n+2}) of strength v exhibits optimal scrambling in the strongly interacting chiral phase |v| > 2|u|, by establishing that its Lyapunov exponent extracted from regularised out-of-time-ordered correlators saturates the chaos bound, specifically λ = 2π T (v/2) at low temperatures.

Background

The paper presents a chiral spin-chain model that simulates key aspects of black hole physics relevant to the Hayden-Preskill teleportation protocol, including Hawking radiation and rapid information scrambling. Numerical studies using exact diagonalisation and an efficient Krylov subspace method indicate that, in the strongly interacting regime |v| > 2|u|, the model’s Lyapunov exponent approaches the expected optimal scrambling bound λ = 2π T (v/2) at low temperatures, consistent with the behavior of quantum black holes.

While these results provide strong numerical evidence, the authors highlight that an analytic proof is presently lacking. Establishing such a proof would firmly validate the chiral spin-chain as an optimal scrambler and strengthen its connection to semiclassical gravity and black hole thermodynamics. The authors suggest field-theoretic approaches, such as bosonisation, as potential avenues to derive this result analytically.