Exact Solvability and Integrability Signatures in a Periodically Driven Infinite-Range Spin Chain: The Case of Floquet interval $π/2$
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2025
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| author | Sharma, Harshit Rout, Sashmita Purohit, Avadhut V. Bhosale, Udaysinh T. |
| author_facet | Sharma, Harshit Rout, Sashmita Purohit, Avadhut V. Bhosale, Udaysinh T. |
| contents | We study the signatures of quantum integrability (QI) in a spin chain model, having infinite-range Ising interaction and subjected to a periodic pulse of an external magnetic field. We analyze the unitary operator, its eigensystem, the single-qubit reduced density matrix, and the entanglement dynamics for arbitrary initial state for any $N$. The QI in our model can be identified through key signatures such as the periodicity of entanglement dynamics and the time-evolved unitary operator, and highly degenerated spectra or Poisson statistics. In our previous works, these signatures were observed in the model for parameters $τ=π/4$ and $J=1,1/2$, where we provided exact analytical results up to $12$ qubits and numerically for large $N$ [Phys. Rev. B \textbf{110}, 064313,(2024)}; arXiv:2411.16670 (2024)}]. In this paper, we extend the analysis to $τ=mπ/2$, and arbitrary $J$ and $N$. We show that the signatures of QI persist for the rational $J$, whereas for irrational $J$, these signatures are absent for any $N$. Further, we perform spectral statistics and find that for irrational $J$, as well as for rational $J$ with perturbations, the spacing distributions of eigenvalues follow Poisson statistics. The average adjacent gap ratio is obtained as $\langle r \rangle=0.386$, consistent with Poisson statistics. Additionally, we compute the ratio of eigenstate entanglement entropy to its maximum value ($\langle S \rangle /S_{Max}$) and find that it remains significantly below $1$ in the limit $N\rightarrow \infty$, which further confirms the QI. We discuss some potential experimental realizations of our model. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2509_19991 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Exact Solvability and Integrability Signatures in a Periodically Driven Infinite-Range Spin Chain: The Case of Floquet interval $π/2$ Sharma, Harshit Rout, Sashmita Purohit, Avadhut V. Bhosale, Udaysinh T. Quantum Physics Other Condensed Matter Mathematical Physics Exactly Solvable and Integrable Systems Computational Physics We study the signatures of quantum integrability (QI) in a spin chain model, having infinite-range Ising interaction and subjected to a periodic pulse of an external magnetic field. We analyze the unitary operator, its eigensystem, the single-qubit reduced density matrix, and the entanglement dynamics for arbitrary initial state for any $N$. The QI in our model can be identified through key signatures such as the periodicity of entanglement dynamics and the time-evolved unitary operator, and highly degenerated spectra or Poisson statistics. In our previous works, these signatures were observed in the model for parameters $τ=π/4$ and $J=1,1/2$, where we provided exact analytical results up to $12$ qubits and numerically for large $N$ [Phys. Rev. B \textbf{110}, 064313,(2024)}; arXiv:2411.16670 (2024)}]. In this paper, we extend the analysis to $τ=mπ/2$, and arbitrary $J$ and $N$. We show that the signatures of QI persist for the rational $J$, whereas for irrational $J$, these signatures are absent for any $N$. Further, we perform spectral statistics and find that for irrational $J$, as well as for rational $J$ with perturbations, the spacing distributions of eigenvalues follow Poisson statistics. The average adjacent gap ratio is obtained as $\langle r \rangle=0.386$, consistent with Poisson statistics. Additionally, we compute the ratio of eigenstate entanglement entropy to its maximum value ($\langle S \rangle /S_{Max}$) and find that it remains significantly below $1$ in the limit $N\rightarrow \infty$, which further confirms the QI. We discuss some potential experimental realizations of our model. |
| title | Exact Solvability and Integrability Signatures in a Periodically Driven Infinite-Range Spin Chain: The Case of Floquet interval $π/2$ |
| topic | Quantum Physics Other Condensed Matter Mathematical Physics Exactly Solvable and Integrable Systems Computational Physics |
| url | https://arxiv.org/abs/2509.19991 |