Entanglement properties of the nontrivial Haldane insulator in the 1D extended Bose-Hubbard model

We investigate the entanglement properties of a nontrivial topological phase in the one-dimensional (1D) Bose-Hubbard model with additional nearest-neighbor repulsion. Employing the large-scale density-matrix renormalization group technique we show that a gapped insulating phase protected by lattice inversion symmetry, the so-called Haldane insulator, appears between the Mott and density wave phases in the intermediate-coupling regime. The phase boundaries were determined from the central charge via the von Neumann entropy. The Haldane insulator reveals a characteristic degeneracy in the entanglement spectra. Breaking the lattice inversion symmetry strongly affects the distinctive gapped dispersion of the dynamical charge response of the bosonic Haldane insulator.