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Entanglement entropy, fidelity and the phase transition of one-dimensional hard-core bosonic system with three-body interactions

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.