Optimally scrambling chiral spin-chain with effective black hole geometry

TL;DR

This paper models a chiral spin-chain that mimics black hole interior physics, demonstrating optimal quantum scrambling and chaos behavior through numerical analysis of Lyapunov exponents.

Contribution

It introduces a condensed matter model capturing black hole-like chaotic dynamics and reveals temperature-dependent scrambling behavior within the black hole analogy.

Findings

Lyapunov exponent increases linearly with temperature inside the black hole region.

Outside the black hole region, the spin-chain shows quadratic temperature dependence.

The model provides insights into quantum chaos and black hole physics.

Abstract

There is currently significant interest in emulating the essential characteristics of black holes, such as their Hawking radiation or their optimal scrambling behavior, using condensed matter models. In this article, we investigate a chiral spin-chain, whose mean field theory effectively captures the behavior of Dirac fermions in the curved spacetime geometry of a black hole. We find that within the region of the chain that describe the interior of the black hole, strong correlations prevail giving rise to many-body chaotic dynamics. Employing out-of-time-order correlations as a diagnostic tool, we numerically compute the associated Lyapunov exponent. Intriguingly, we observe a linear increase in the Lyapunov exponent with temperature within the black hole's interior at low temperatures, indicative of optimal scrambling behavior. This contrasts with the quadratic temperature dependence exhibited by the spin-chain on the region outside the black hole. Our findings contribute to a deeper understanding of the interplay between black hole geometry and quantum chaos, offering insights into fundamental aspects of quantum gravity.