  We numerically study quantum chaos properties of long-range XXZ dipolar
Hamiltonian spin systems. Two geometries are considered: (i) an open chain with
19 spins, (ii) a face-centered cubic lattice with 14 spins. Energy
level-spacing distribution indicates that the three-dimensional geometry is
highly chaotic, while the one-dimensional system is mildly chaotic for small
chains, but has increasing chaoticity for larger chains. We also look at
statistical properties of energy eigenvectors, and of one- and two-body local
observables. Finally, we present some preliminary results on time-evolution,
local spin dynamics and thermalization. Quantum chaos may have important
implications for "scrambling" of quantum information, in both condensed matter
systems and in astrophysical applications such as black holes.
