Critical points of the Bose–Hubbard model with three-body local interaction

•We studied the Bose–Hubbard model with a local three-body interaction term.•We show that the Mott insulator lobes always grow as a function of the density.•We found a power law dependence of the critical point position with the density.

Using the density matrix renormalization group method, we study a one-dimensional system of bosons that interact with a local three-body term. We calculate the phase diagram for higher densities, where the Mott insulator lobes are surrounded by the superfluid phase. We also show that the Mott insulator lobes always grow as a function of the density. The critical points of the Kosterlitz–Thouless transitions were determined through the von Neumann block entropy, and its dependence on the density is given by a power law with a negative exponent.