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This research analytically demonstrates robust signatures of quantum integrability in a periodically driven $p$-spin kicked top model, revealing specific spectral clustering and entanglement dynamics that persist across varying kicking strengths. The study provides critical theoretical benchmarks for understanding chaotic versus regular regimes in infinite-range spin systems, which are relevant to the design of fault-tolerant quantum simulators and error-corrected hardware. While experimental realizations are discussed, the core contribution remains a rigorous mathematical characterization of integrability conditions in driven many-body quantum systems.
Exact Solvability and Integrability Signatures in a Periodically Driven Infinite-Range $p$-Spin Kicked Top Model
arXiv:2509.19991v2 Announce Type: replace Abstract: We study the signatures of quantum integrability (QI) in a $p$-spin kicked top model with infinite-range Ising interactions, subjected to periodic pulses of an external magnetic field, with the precession angle fixed at $\alpha=m\pi$. We analytically compute the unitary operator, its eigensystem, time evolution, single-qubit reduced density matrix, and entanglement dynamics for arbitrary initial states. We show that the spectrum of the unitary operator exhibits pronounced clustering of eigenphases in some regions, leading to strongly non-uniform spectral features with $p$. The entanglement measures and unitary operator dynamics exhibit periodic behavior, while the eigenvalue spectrum shows strong degeneracies when the kicking strength $k'$ is a rational multiple of $\pi$ for even $p$. For odd $p$, both the periodic behavior and spectral degeneracies persist for all values of $k'$. This periodic behavior extends to the strong-kicking regime ($k'=J j^{p-1}\pi$), where for rational values of $J$ the dynamics remain periodic. For any $k'$ and $p$ the spectral statistics shows Poissonian behavior and the average adjacent gap ratio $\langle r \rangle = 2\ln 2 - 1$, consistent with integrable behaviour. The spectral form factor further supports this nature. Additionally, we compute the ratio of average eigenstate entanglement entropy to its maximum value ($\langle S \rangle /S_{Max}$) and find that it remains significantly far below from $1$ in the limit $N\rightarrow \infty$. These results collectively establish robust signatures of QI across all $k', p,$ and system sizes. We also discuss possible experimental realizations of the model.
Abstract: We study the signatures of quantum integrability (QI) in a $p$-spin kicked top model with infinite-range Ising interactions, subjected to periodic pulses of an external magnetic field, with the precession angle fixed at $\alpha=m\pi$. We analytically compute the unitary operator, its eigensystem, time evolution, single-qubit reduced density matrix, and entanglement dynamics for arbitrary initial states. We show that the spectrum of the unitary operator exhibits pronounced clustering of eigenphases in some regions, leading to strongly non-uniform spectral features with $p$. The entanglement measures and unitary operator dynamics exhibit periodic behavior, while the eigenvalue spectrum shows strong degeneracies when the kicking strength $k'$ is a rational multiple of $\pi$ for even $p$. For odd $p$, both the periodic behavior and spectral degeneracies persist for all values of $k'$. This periodic behavior extends to the strong-kicking regime ($k'=J j^{p-1}\pi$), where for rational values of $J$ the dynamics remain periodic. For any $k'$ and $p$ the spectral statistics shows Poissonian behavior and the average adjacent gap ratio $\langle r \rangle = 2\ln 2 - 1$, consistent with integrable behaviour. The spectral form factor further supports this nature. Additionally, we compute the ratio of average eigenstate entanglement entropy to its maximum value ($\langle S \rangle /S_{Max}$) and find that it remains significantly far below from $1$ in the limit $N\rightarrow \infty$. These results collectively establish robust signatures of QI across all $k', p,$ and system sizes. We also discuss possible experimental realizations of the model.
20 pages (two-column) + 17 figures. Generalized from the kicked-top model to the $p$-spin case, including arbitrary $k'$ at $\alpha=\pi$ and regimes where a classical limit does not exist; signatures of quantum integrability are established. Comments welcome
Quantum Physics (quant-ph); Other Condensed Matter (cond-mat.other); Mathematical Physics (math-ph); Exactly Solvable and Integrable Systems (nlin.SI); Computational Physics (physics.comp-ph)
arXiv:2509.19991 [quant-ph]
(or arXiv:2509.19991v2 [quant-ph] for this version)
From: Udaysinh T. Bhosale [view email] [v1] Wed, 24 Sep 2025 10:50:56 UTC (475 KB) [v2] Tue, 29 Sep 2026 10:58:16 UTC (6,054 KB)
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