Floquet thermalization by power-law induced permutation symmetry breaking

Abstract

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 $1/r^α$, we break this symmetry with a non-zero $α$. 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 $x$ direction subjected to periodic kicks in transverse direction. As we increase $α$, the system interpolates from an infinite range spin system at $α=0$ exhibiting permutation symmetry, to a short range integrable model as $α\rightarrow \infty$ where this permutation symmetry is absent. We focus on this change in the behavior of the system as $α$ is tuned, using dynamical quantities like total angular momentum and von Neumann entropy. Starting from the chaotic limit of the permutation symmetric Hamiltonian at $α=0$, for the finite system sizes considered, we find that for small $α$, the steady state values of these quantities remain close to the permutation symmetric subspace values corresponding to $α=0$. At intermediate $α$ values, these show signatures of thermalization exhibiting values corresponding to that of random states in full Hilbert space. On the other hand, the large $α$ limit approaches the values corresponding to integrable kicked Ising model. In addition, we also study the dependence of thermalization on the driving period $τ$, with results indicating the onset of thermalization for smaller values of $α$ when $τ$ is large, thereby extending the thermalizing window in the intermediate range of $α$. We further confirm these results using effective dimension and spectral statistics.