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 $1/r^{\alpha }$, we break this symmetry with a non-zero $\alpha$. 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 $x$ direction subjected to periodic kicks in 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 like 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 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 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.

11 pages, 10 figures

References in corpus (22)

• Localization of interacting fermions at high temperature
• The distribution of the ratio of consecutive level spacings in random matrix ensembles
• Equilibrium states of generic quantum systems subject to periodic driving
• Many-body localization in periodically driven systems
• Periodically driven ergodic and many-body localized quantum systems
• Diluted one-dimensional spin glasses with power law decaying interactions
• Chaos, entanglement and decoherence in the quantum kicked top
• Tuning anomalous Floquet topological bands with ultracold atoms
• Classical approaches to prethermal discrete time crystals in one, two, and three dimensions
• Statistics of phase space localization measures and quantum chaos in the kicked top model
• Floquet time crystals in driven spin systems with all-to-all $p$-body interactions
• Protocol using kicked Ising dynamics for generating states with maximal multipartite entanglement
• Theory of robust quantum many-body scars in long-range interacting systems
• Spin Squeezing, Negative Correlations, and Concurrence in the Quantum Kicked Top Model
• Prethermal nematic order and staircase heating in a driven frustrated Ising magnet with dipolar interactions
• Slow thermalization and subdiffusion in $U(1)$ conserving Floquet random circuits
• Sharp detection of the onset of Floquet heating using eigenstate sensitivity
• Mimicking quantum correlation of a long-range Hamiltonian by finite-range interactions
• Digital Quantum Simulation, Learning of the Floquet Hamiltonian, and Quantum Chaos of the Kicked Top
• Quantum Chaos, Randomness and Universal Scaling of Entanglement in Various Krylov Spaces
• Chaos controlled and disorder driven phase transitions induced by breaking permutation symmetry
• Insights from the exact analytical solution of periodically driven transverse field Ising chain