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

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Keles A., Zhao E., Liu W. V.

PHYSICAL REVIEW A, vol.99, no.5, 2019 (Peer-Reviewed Journal) identifier identifier

  • Publication Type: Article / Article
  • Volume: 99 Issue: 5
  • Publication Date: 2019
  • Doi Number: 10.1103/physreva.99.053620
  • Journal Name: PHYSICAL REVIEW A
  • Journal Indexes: Science Citation Index Expanded, Scopus


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.