Higher-order level spacings in random matrix theory based on Wigner's conjecture

Abstract

The distribution of higher order level spacings, i.e. the distribution of $\{s_i^{(n)}=E_{i+n}-E_i\}$ with $n\ge 1$ is derived analytically using a Wigner-like surmise for Gaussian ensembles of random matrix as well as Poisson ensemble. It is found $s^{(n)}$ in Gaussian ensembles follows a generalized Wigner-Dyson distribution with rescaled parameter $\alpha =\nu C_{n+1}^2+n-1$, while that in Poisson ensemble follows a generalized semi-Poisson distribution with index $n$. Numerical evidences are provided through simulations of random spin systems as well as non-trivial zeros of Riemann zeta function. The higher order generalizations of gap ratios are also discussed.

7 pages, 4 figures

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• Localization of interacting fermions at high temperature
• Many-body localization edge in the random-field Heisenberg chain
• The distribution of the ratio of consecutive level spacings in random matrix ensembles
• Many-Body Localization in a Quasiperiodic System
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Cited by in corpus (2)

• Random Matrix Theory of the Isospectral twirling
• Critical Level Statistics at the Many-Body Localization Transition Region