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