Permutation symmetry plays a central role in the understanding of collective quantum dynamics. By introducing power-law couplings that algebraically decay with the distance between the spins $r$ as $1/r^{\alpha }$, we break this symmetry with a nonzero $\alpha$. This allows us to probe the emergence of new dynamical behaviors, including thermalization in an otherwise permutation symmetric Hamiltonian with all-to-all spin interactions along the $x$ direction subjected to periodic kicks in the transverse direction. As we increase $\alpha$, the system interpolates from an infinite-range spin system at $\alpha =0$ exhibiting permutation symmetry to a short-range integrable model as $\alpha \to \infty$ where this permutation symmetry is absent. We focus on this change in the behavior of the system as $\alpha$ is tuned, using dynamical quantities such as total angular momentum and von Neumann entropy. Starting from the chaotic limit of the permutation symmetric Hamiltonian at $\alpha =0$, for the finite system sizes that are considered, we find that for small $\alpha$, the steady-state values of these quantities remain close to the permutation symmetric subspace values corresponding to $\alpha =0$. At intermediate $\alpha$ values, these show signatures of thermalization exhibiting values corresponding to that of random states in full Hilbert space. On the other hand, the large $\alpha$ limit approaches the values corresponding to the integrable kicked Ising model. In addition, we also study the dependence of thermalization on the driving period $\tau$, with results indicating the onset of thermalization for smaller values of $\alpha$ when $\tau$ is large, thereby extending the thermalizing window in the intermediate range of $\alpha$. We further confirm these results using effective dimension and spectral statistics.

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• Quantum chaos
• Quantum correlations in quantum information