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The statistics of gap ratios between consecutive energy levels is a widely used tool, in particular in the context of many-body physics, to distinguish between chaotic and integrable systems, described respectively by Gaussian ensembles of random matrices and Poisson statistics.
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On a more algebraic note, the decomposition of the RSOS space into F L + 1 F_{L+1} and F L − 1 F_{L-1} can be understood as a decomposition into irreducible representations of the periodic Temperley-Lieb algebra Pasquier and Saleur 1990 . More recently, it has been observed that the two orthogonal subspaces of the periodic RSOS model can be obtained from the open
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