Recent studies have suggested a new phase in the extended Bose-Hubbard model in one dimension at integer filling. In this work, we show that this new phase is phase-separated into a supersolid and superfluid part, generated by mechanical instability. Numerical simulations are performed by means of the density matrix renormalization group algorithm in terms of matrix product states. In the phase-separated phase and the adjacent homogeneous superfluid and supersolid phases, we find peculiar spatial patterns in the entanglement spectrum and string-order correlation functions and show that they survive in the thermodynamic limit. In particular, we demonstrate that the elementary excitations of the homogeneous superfluid with enhanced periodic modulations are phonons, find the central charge to be
c=1, and show that the velocity of sound, extracted from the intrinsic level splitting for finite systems, matches with the propagation velocity of local excitations in dynamical simulations. This suggests that the low-energy spectrum of the phase under investigation is effectively captured by a spinless Luttinger liquid, for which we find consistent results between the Luttinger parameter obtained from the linear dependence of the structure factor and the algebraic decay of the one-body density matrix.
We study the stability of superflow of Bose gases in optical lattices by analyzing the Bose-Hubbard model within the Gutzwiller mean-field approximation. We calculate the excitation spectra of the homogeneous Bose-Hubbard model at unit filling to determine the critical momenta for the Landau and dynamical instabilities. These two critical momenta are shown to approach each other when the on-site interaction increases towards the Mott transition point. In order to make a direct connection with realistic experiments, we next take into account a parabolic trapping potential and compute the real-time dynamics of dipole oscillations induced by suddenly displacing the trap center. We consider the following two cases: standard soft-core bosons, whose interparticle interactions include the on-site one only; and hard-core bosons with long-range dipole-dipole interactions. For both cases, we show that the dipole oscillation is significantly damped when the maximum local momentum exceeds a certain threshold, which quantitatively agrees with the critical momentum for the dynamical instability in the homogeneous system. In the case of dipolar hard-core bosons, the dynamical instability of dipole oscillations leads to the formation of checkerboard density waves in the superfluid phase near the boundary to the supersolid phase.