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Spectrum and completeness of the 3 state superintegrable chiral Potts model

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We find the rules which count the energy levels of the three-state superintegrable chiral Potts model and demonstrate that these rules are complete. In the massive phase we show that the spectrum can be written in terms of two single-particle levels where one of the levels has the unusual property that it exists only for a limited range of momentum. We also discuss the relation of the counting rules to the S = 1 XXZ spin chain with anisotropy gamma = 3.

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