Dipolarly-Coupled Chaotic Quantum Spin Systems

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.