Superposition and higher-order spacing ratios in random matrix theory with application to complex systems

@article{Bhosale2021SuperpositionAH,
  title={Superposition and higher-order spacing ratios in random matrix theory with application to complex systems},
  author={Udaysinh T. Bhosale},
  journal={Physical Review B},
  year={2021}
}
The joint distribution of every second eigenvalue obtained after superposing the spectra of two circular orthogonal ensembles ($\beta=1$) is known to be equal to that of the circular unitary ensemble ($\beta=2$), where the parameter $\beta$ is the Dyson index of the ensemble. Superposition of spectra of $m$ such circular orthogonal ensembles is studied numerically using higher-order spacing ratios. It is conjectured that the joint probability distribution of every $k=m-2$-th $(m\geq4… 
Probing Symmetries of Quantum Many-Body Systems through Gap Ratio Statistics
TLDR
The approach furnishes an efficient way to characterize the number and size of independent symmetry subspaces, and presents a large set of applications in many-body physics, ranging from quantum clock models and anyonic chains to periodically-driven spin systems.

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