We derive the explicit analytical results of low-lying eigenenergies, eigenstates, momentum distributions, and all the two-order spatial correlation functions for a Bose–Hubbard model on a ring in the strong interaction limit by means of the first-order perturbation theory. We show explicitly that the ground and the low-lying excited states are all quantum entangled states in the incommensurate filling case and that certain correlation functions in some of these states, the ground state in particular, violate the Schwarz inequality, another indication of their nonclassicality.
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