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Is there a quantum many-body system that scrambles information as fast as ablack hole? The Sachev-Ye-Kitaev model can saturate the conjectured bound forchaos, but it requires random all-to-all couplings of Majorana fermions thatare hard to realize in experiments. Here we examine a quantum spin model ofrandomly oriented dipoles where the spin exchange is governed by dipole-dipoleinteractions. The model is inspired by recent experiments on dipolar spinsystems of magnetic atoms, dipolar molecules, and nitrogen-vacancy centers. Wemap out the phase diagram of this model by computing the energy levelstatistics, spectral form factor, and out-of-time-order correlation (OTOC)functions. We find a broad regime of many-body chaos where the energy levelsobey Wigner-Dyson statistics and the OTOC shows distinctive behaviors atdifferent times: Its early-time dynamics is characterized by an exponentialgrowth, while the approach to its saturated value at late times obeys a powerlaw. The temperature scaling of the Lyapunov exponent $\lambda_L$ shows thatwhile 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 ofspins.

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