Sashmita Rout | Searcharxiv

arXiv2025

Higher-order spacings in the superposed spectra of random matrices with comparison to spacing ratios and application to complex systems

Higher-order spacing statistics in the $m$ superposed spectra of circular random matrices of the same class are studied numerically. We conjecture that for given $m$ (or order $k$) and $\beta$, the sequence of modified Dyson index $\beta'(k)$ (or $\beta'(m)$) obtained using the sum of absolute differences between the cumulative distribution functions method (denoted as $D(\beta')$) is unique. Also, for a given $k$, the distribution tends to the corresponding $k$-th order Poisson statistics in the limit $m\rightarrow \infty$. The quantum chaotic kicked top model for various Hilbert space dimensions is studied, and it is found to satisfy our conjecture. This involves the numerical verification of $m=2$ case of COE results. Our result can be used as a tool for the characterization of a system and to determine the symmetry structure of the system without desymmetrization of the spectra. Additionally, the comparative study of the higher-order spacing and ratio distributions in both $m=1$ and $m=2$ cases of COE as well as GOE is performed within and across these ensembles numerically using the $D(\beta')$ method. This study is carried out both by varying the dimension and keeping the number of realizations constant, and vice-versa. The same asymptotic higher-order statistics are observed across COE and GOE in terms of a given spectral fluctuation measure. But, within a given ensemble of COE or GOE, the results of higher-order spacing and ratio distributions agree with each other only up to some lower $k$, and beyond that, they start deviating from each other. Further, the spectral fluctuations of the intermediate map of various dimensions are studied. Various important observations and discussions from the analysis of our extensive numerical computations are presented.

physics.data-an↗

arXiv2025

Exact Solvability and Integrability Signatures in a Periodically Driven Infinite-Range Spin Chain: The Case of Floquet interval $\pi/2$

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 $\tau=\pi/4$ 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 $\tau=m\pi/2$, 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.

quant-ph↗