Dipolarly-Coupled Chaotic Quantum Spin Systems

TL;DR

This study investigates quantum chaos in long-range dipolar XXZ spin systems across different geometries, revealing geometry-dependent chaotic behavior and exploring implications for quantum information scrambling.

Contribution

It provides the first numerical analysis of quantum chaos in 3D dipolar spin systems, comparing open chain and cubic lattice geometries.

Findings

3D geometry exhibits high quantum chaos

1D chains show increasing chaos with size

Preliminary results on thermalization and spin dynamics

Abstract

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.