Abstract 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.
We employ the (dynamical) density-matrix renormalization-group technique to investigate the ground-state properties of the Bose-Hubbard model with nearest-neighbor transfer amplitudes
t and local two-body and three-body repulsion of strength
U and
W, respectively. We determine the phase boundaries between the Mott-insulating and superfluid phases for the lowest two Mott lobes from the chemical potentials. We calculate the tips of the Mott lobes from the Tomonaga-Luttinger liquid parameter and confirm the positions of the Kosterlitz-Thouless points from the von Neumann entanglement entropy. We find that physical quantities in the second Mott lobe such as the gap and the dynamical structure factor scale almost perfectly in
t/(U+W), even close to the Mott transition. Strong-coupling perturbation theory shows that there is no true scaling but deviations from it are quantitatively small in the strong-coupling limit. This observation should remain true in higher dimensions and for not too large attractive three-body interactions.
We carry out an extensive study of the phase diagram of the extended Bose Hubbard model, with a mean filling of one boson per site, in one dimension by using the density matrix renormalization group and show that it can have Superfluid (SF), Mott-insulator (MI), density-wave (DW) and Haldane-insulator (HI) phases depending on the precise value of filling and how edge states are handled. We show that the critical exponents and central charge for the HI-DW, MI-HI and SF-MI transitions are consistent with those for models in the two-dimensional Ising, Gaussian, and Berezinskii-Kosterlitz-Thouless (BKT) universality classes, respectively; and we suggest that the SF-HI transition may be more exotic than a simple BKT transition.
We carry out an extensive study of the phase diagrams of the extended Bose Hubbard model, with a mean filling of one boson per site, in one dimension by using the density matrix renormalization group and show that it contains Superfluid (SF), Mott-insulator (MI), density-wave (DW) and Haldane-insulator (HI) phases. We show that the critical exponents and central charges for the HI-DW, MI-HI and SF-MI transitions are consistent with those for models in the two-dimensional Ising, Gaussian, and Berezinskii-Kosterlitz-Thouless (BKT) universality classes, respectively; and we suggest that the SF-HI transition may be more exotic than a simple BKT transition. We show explicitly that different boundary conditions lead to different phase diagrams.
We use the finite-size, density-matrix-renormalization-group (FSDMRG) method to obtain the phase diagram of the one-dimensional
(d=1) extended Bose-Hubbard model for density $\ensuremath{\rho}=1$ in the $U\ensuremath{-}V$ plane, where
U and
V are, respectively, onsite and nearest-neighbor interactions. The phase diagram comprises three phases: superfluid (SF), Mott insulator (MI), and mass-density-wave (MDW). For small values of
U and
V, we get a reentrant SF-MI-SF phase transition. For intermediate values of interactions the SF phase is sandwiched between MI and MDW phases with continuous SF-MI and SF-MDW transitions. We show, by a detailed, finite-size scaling analysis, that the MI-SF transition is of Kosterlitz-Thouless (KT) type whereas the MDW-SF transition has both KT and two-dimensional Ising characters. For large values of
U and
V we get a direct, first-order, MI-MDW transition. The MI-SF, MDW-SF, and MI-MDW phase boundaries join at a bicritical point at $(U,V)=(8.5\ifmmode\pm\else\textpm\fi{}0.05,4.75\ifmmode\pm\else\textpm\fi{}0.05)$.
Using the density matrix renormalization group method, we determine the phase diagram of the Bose-Hubbard model with local two- and three-body interactions, describing polar molecules in one-dimensional optical lattices. The difference in the block von Neumann entropy with different system sizes was used to establish the critical points. We found that the quantum critical point position increases with the three-body interaction. We show that the model studied is in the same universality class as the model with pure two-body interactions.