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A quantum phase transition driven by the statistics was observed in ananyon-Hubbard model with local three-body interactions. Using a fractionalJordan-Wigner transformation, we arrived at a modified Bose-Hubbard model,which exhibits Mott insulator and superfluid phases. The absence of a Mottinsulator state with one particle per site depends on the anyonic angle, and aquantum phase transition from a superfluid to a Mott insulator state isobtained for a fixed value of the hopping. The critical points were estimatedwith the von Neumann block entropy and increase as the hopping grows. Thestatistics modify the ground state, and three different superfluid regions wereobserved for larger values of the anyonic angle.

Three-body interaction effects on the ground state of one-dimensional anyons