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For a one-dimensional model in which the two-body interactions are long-range and strong, the system almost crystallizes. The harmonic modes of such a lattice were used by Krivnov and Ovchinnikov to compute the ground-state wave function and the dynamical density-density correlations.

Density-density correlations in a Luttinger liquid: Lattice approximation in the Calogero-Sutherland model