  The extended Bose-Hubbard model with pure three-body local interactions is
studied using the Density Matrix Renormalization Group approach. The shapes of
the first two insulating lobes are discussed, and the values of the critical
tunneling for which the system undergoes the quantum phase transition from
insulating to superfluid phase are predicted. It is shown that stability of
insulating phases, in contrast to the standard Bose-Hubbard model, is enhanced
for larger fillings. It is also shown that, on the tip of the boundary of the
insulating phase, the model under consideration belongs to the
Berenzinskii-Kosterlitz-Thouless universality class.
