  We study the one-dimensional hard-core Bose-Hubbard model with three-body
interactions. In previous work[1], the two-thirds filling solid with both
bond-wave order (BOW) and charge-density wave order (CDW) is found and it
undergoes a second order phase transition to the superfluid phase. However, in
recent work[2], we found the BOW not independent with CDW order. Thus, by
utilizing the density matrix renormalization group, we make use of both
entanglement entropy and fidelity susceptibility to detect the phase
transition. In two-thirds filling, the extreme point of the entanglement
entropy also indicates the superfluid phase transition point. However, the
pairwise entanglement entropy drop quickly after additional critical point,
such disentangled behaviour demonstrates another melting point to the CDW
phase. Thus, a novel intermediate phase between CDW phase and superfluid phase
is found. At last, we analyzed the half filling case with entanglement entropy.
