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arXiv · 2401.09524

Size Winding Mechanism beyond Maximal Chaos

Tian-Gang Zhou·Yingfei Gu·Pengfei Zhang
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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.

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Tian-Gang Zhou, Yingfei Gu, Pengfei Zhang. 2024-01-17. Size Winding Mechanism beyond Maximal Chaos. https://doi.org/10.1007/jhep11(2024)044

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