Scrambling dynamics and many-body chaos in a random dipolar spin model

TL;DR

This paper investigates a dipolar spin model inspired by experiments, revealing a broad regime of many-body chaos with dynamics that approach the black hole chaos bound at low temperatures and large system sizes.

Contribution

It introduces a dipolar spin model exhibiting many-body chaos, bridging theoretical chaos bounds with experimentally relevant systems.

Findings

The model shows Wigner-Dyson level statistics indicating chaos.

OTOC exhibits exponential growth and power-law saturation behaviors.

Lyapunov exponent approaches the chaos bound at low temperatures and large N.

Abstract

Is there a quantum many-body system that scrambles information as fast as a black hole? The Sachev-Ye-Kitaev model can saturate the conjectured bound for chaos, but it requires random all-to-all couplings of Majorana fermions that are hard to realize in experiments. Here we examine a quantum spin model of randomly oriented dipoles where the spin exchange is governed by dipole-dipole interactions. The model is inspired by recent experiments on dipolar spin systems of magnetic atoms, dipolar molecules, and nitrogen-vacancy centers. We map out the phase diagram of this model by computing the energy level statistics, spectral form factor, and out-of-time-order correlation (OTOC) functions. We find a broad regime of many-body chaos where the energy levels obey Wigner-Dyson statistics and the OTOC shows distinctive behaviors at different times: Its early-time dynamics is characterized by an exponential growth, while the approach to its saturated value at late times obeys a power law. The temperature scaling of the Lyapunov exponent $\lambda_L$ shows that while it is well below the conjectured bound $2\pi T$ at high temperatures, $\lambda_L$ approaches the bound at low temperatures and for large number of spins.