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We introduce a notion of local level spacings and study their statisticswithin a random-matrix-theory approach. In the limit of infinite-dimensionalrandom matrices, we identify the two universal classes of local spacingsdistributions which describe unfolded spectra of quantum systems with fullychaotic and completely integrable classical dynamics, respectively. We furtherargue, and explicitly demonstrate by exact diagonalisation of theSachdev-Ye-Kitaev (SYK) Hamitonians, that the ratios of averaged local spacingscomputed for raw spectra maintain their universality thus offering a frameworkto monitor spectral statistics in quantum many-body systems.

Statistics of local level spacings in quantum chaology