Size Winding Mechanism beyond Maximal Chaos

Abstract

The concept of information scrambling elucidates the dispersion of local information in quantum many-body systems, offering insights into various physical phenomena such as wormhole teleportation. This phenomenon has spurred extensive theoretical and experimental investigations. Among these, the size-winding mechanism emerges as a valuable diagnostic tool for optimizing signal detection. In this work, we establish a computational framework for determining the winding size distribution in large-$N$ quantum systems with all-to-all interactions, utilizing the scramblon effective theory. We obtain the winding size distribution for the large-$q$ SYK model across the entire time domain. Notably, we unveil that the manifestation of size winding results from a universal phase factor in the scramblon propagator, highlighting the significance of the Lyapunov exponent. These findings contribute to a sharp and precise connection between operator dynamics and the phenomenon of wormhole teleportation.

v2: 15 pages, 5 figures. v1: 6 pages, 4 figures, Supplemental Material: 4 pages, 1 figure