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arXiv:cond-mat/0407011 · Physical Review B

Superfluid, Mott-insulator, and mass-density-wave phases in the one-dimensional extended Bose-Hubbard model

Ramesh V. Pai, Rahul Anil Pandit

Published Mar 15, 2005• 40 citations
arXivHTMLPDF

Abstract

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 $(U,V)=(8.5\ifmmode\pm\else\textpm\fi{}0.05,4.75\ifmmode\pm\else\textpm\fi{}0.05)$.

DOI
10.1103/physrevb.71.104508

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We use the finite-size, density-matrix-renormalization-group (FSDMRG) method to obtain the phase diagram of the one-dimensional (d=1)(d=1)(d=1) extended Bose-Hubbard model for density \ensuremathρ=1\ensuremath{\rho}=1\ensuremathρ=1 in the U\ensuremath−VU\ensuremath{-}VU\ensuremath−V plane, where UUU and VVV 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 UUU and VVV, 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 UUU and VVV 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±\else\textpm\fi0.05,4.75\ifmmode±\else\textpm\fi0.05)(U,V)=(8.5\ifmmode\pm\else\textpm\fi{}0.05,4.75\ifmmode\pm\else\textpm\fi{}0.05)(U,V)=(8.5\ifmmode±\else\textpm\fi0.05,4.75\ifmmode±\else\textpm\fi0.05).
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 study the one-dimensional extended Bose-Hubbard model in incommensurate densities using the density matrix renormalization group with the mean-filed (CMFT+DMRG)and density matrix renormalization group (DMRG) methods. We focus on the region of the phase diagram where onsite interaction (U) is smaller than the nearest-neighbor interaction (V). We determine the superfluid and the density wave order parameters to identify superfluid, phase-separated, supersolid, density wave phases, and obtain the phase diagram in the density-onsite interaction(ρ, U) plane for fixed nearest-neighbor interaction. The supersolid and phase-separation phases exist for a wide range of densities. The density ranges for which the phase-separation is seen shrinking with theincrease in the onsite interaction.
We study the one-dimensional Bose-Hubbard model using the density-matrix renormalization group. For the cases of on-site interactions and additional nearest-neighbor interactions the phase boundaries of the Mott insulators and charge-density wave phases are determined. We find a direct phase transition between the charge-density wave phase and the superfluid phase, and no supersolid or normal phases. In the presence of nearest-neighbor interaction the charge density wave phase is completely surrounded by a region in which the effective interactions in the superfluid phase are repulsive. In this region a single impurity causes the system to be insulating. An even bigger region of the superfluid phase is driven into a Bose-glass phase by any finite quenched disorder. We determine the boundaries of both regions in the phase diagram. The ac conductivity of the superfluid phase in the attractive and the repulsive region is calculated, and a big superfluid stiffness is found in the attractive as well as the repulsive region.
We report our findings on the quantum phase transitions in cold bosonic atoms in a one-dimensional optical lattice using the finite-size density-matrix renormalization-group method in the framework of the extended Bose-Hubbard model. We consider wide ranges of values for the filling factors and the nearest-neighbor interactions. At commensurate fillings, we obtain two different types of charge-density wave phases and a Mott insulator phase. However, departure from commensurate fillings yields the exotic supersolid phase where both the crystalline and the superfluid orders coexist. In addition, we obtain the signatures for the solitary waves and the superfluid phase.
We use the density-matrix renormalization group to study the one-dimensional bosonic Hubbard model, with and without disorder. We obtain the gaps in all phases, certain correlation functions, and the superfluid density. A finite-size-scaling analysis enables us to obtain an accurate phase diagram and the $\ensuremath{\beta}$ function at the superfluid--Mott insulator transition and the Kosterlitz-Thouless essential singularity in the pure case. We also obtain coupling constants used in effective field theories for this system.