Competing short-range and long-range interactions represent prominent ingredients for the formation of complex quantum many-body phases. In this respect, the Rydberg atom is promising because the excited state manifold has both density-density and exchange interactions, which can vary significantly in strength and extent. Focusing on one-dimensional systems, we exploit van der Waals interactions and dipole-dipole interactions of Rydberg atoms to obtain zero-temperature phase diagrams for homogeneous chain and dimer models. For uniform chains, the boundary between ordered phases and Luttinger liquids can be influenced, whereas for dimerization, a new type of jointly ordered density-wave phase has been identified, which has been used in the study of physics. The versatility of his Rydberg platform is emphasized. Includes short-range and long-range interactions simultaneously.

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