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We develop a novel approach to understand the phases of one-dimensional Bose-Hubbard models. We integrate the simplicity of the mean-field theory and the numerical power of the density matrix renormalization group method to build an effective numerical technique with moderate computational resources to determine superfluid order parameters and correlation functions of large one-dimensional systems. We demonstrate the applicability of this method to directly identify superfluid, Mott insulator, and density wave phases in Bose-Hubbard models., Comment: 8 pages, 11 figures

We obtain the excitation spectra of the following three generalized Bose-Hubbard (BH) models: (1) a two-species generalization of the spinless BH model, (2) a single-species, spin-1 BH model, and (3) the extended Bose-Hubbard model (EBH) for spinless interacting bosons of one species. In all the phases of these models we provide a unified treatment of random-phase-approximation (RPA) excitation spectra. These spectra have gaps in all the MI phases and gaps in the DW phases in the EBH model; they are gapless in all the SF phases in these models and in the SS phases in the EBH model. We obtain the dependence of (a) gaps $\Delta$ and (b) the sound velocity $u_s$ on the parameters of these models and examine $\Delta$ and $u_s$ as these systems go through phase transitions. At the SF-MI transitions in the spin-1 BH model, $u_s$ goes to zero continuously (discontinuously) for MI phases with an odd (even) number of bosons per site; this is consistent with the natures of these transition in mean-field theory. In the SF phases of these models, our excitation spectra agree qualitatively, at weak couplings, with those that can be obtained from Gross-Pitaevskii-type models. We compare the results of our work with earlier studies of related models and discuss implications for experiments., Comment: 16 pages, 10 figures

We obtain the complete quantum phase diagram of bosons on a two-leg ladder in the presence of attractive onsite and repulsive interchain nearest-neighbor interactions by imposing the onsite three-body constraint. We find three distinct phases; namely, the atomic superfluid (ASF), dimer superfluid (DSF), and the dimer rung insulator (DRI). In the absence of the interchain nearest-neighbor repulsion, the system exhibits a transition from the ASF to the DSF phase with increasing onsite attraction. However, the presence of the interchain nearest-neighbor repulsion stabilizes a gapped DRI phase, which is flanked by the DSF phase. We also obtain the phase diagram of the system for different values of the interchain nearest-neighbor interaction. By evaluating different order parameters, we obtain the complete phase diagram and the properties of the phase transitions using the self-consistent cluster mean-field theory., Comment: 9 pages, 15 figures

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., Comment: Version 2. 15 pages, 14 figures. Extended version of arXiv:1211.5202

We study a system of hardcore boson on a one-dimensional lattice with frustrated next-nearest neighbor hopping and nearest neighbor interaction. At half filling, for equal magnitude of nearest and next-nearest neighbor hopping, the ground state of this system exhibits a first order phase transition from a Bond-Ordered (BO) solid to a Charge-Density-Wave(CDW) solid as a function of the nearest neighbor interaction. Moving away from half filling we investigate the system at incommensurate densities, where we find a SuperSolid (SS) phase which has concurrent off-diagonal long range order and density wave order which is unusual in a system of hardcore bosons in one dimension. Using the finite-size Density-Matrix Renormalization Group (DMRG) method, we obtain the complete phase diagram for this model.

We study a system of hard-core bosons at half-filling in a one-dimensional optical superlattice. The bosons are allowed to hop to nearest and next-nearest neighbor sites producing a zig-zag geometry and we obtain the ground state phase diagram as a function of microscopic parameters using the finite-size density matrix renormalization group (FS-DMRG) method. Depending on the sign of the next-nearest neighbor hopping and the strength of the superlattice potential the system exhibits three different phases, namely the bond-order (BO) solid, the superlattice induced Mott insulator (SLMI) and the superfluid (SF) phase. When the signs of both hopping amplitudes are the same (the "unfrustrated" case), the system undergoes a transition from the SF to the SLMI at a non-zero value of the superlattice potential. On the other hand, when the two amplitudes differ in sign (the "frustrated" case), the SF is unstable to switching on a superlattice potential and also exists only up to a finite value of the next nearest neighbor hopping. This part of the phase diagram is dominated by the BO phase which breaks translation symmetry spontaneously even in the absence of the superlattice potential and can thus be characterized by a bond order parameter. The transition from BO to SLMI appears to be first order., Comment: 6 pages, 11 figures

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., Comment: 5 pages, 2 figures

We study hardcore bosons on a triangular ladder at half filling in the presence of a frustrating hopping term and a competing nearest neighbor repulsion $V$ which promotes crystallization. Using the finite-size density-matrix renormalization group method, we obtain the phase diagram which contains three phases: a uniform superfluid (SF), an insulating charge density wave (CDW) crystal and a bond ordered insulator (BO). We find that the transitions from SF to CDW and SF to BO are continuous in nature, with critical exponents varying continously along the phase boundaries, while the transition from CDW to BO is found to be first order. The phase diagram is also shown to contain an exactly solvable Majumdar Ghosh point, and re-entrant SF to CDW phase transitions., Comment: 10 pages, 16 figures

Motivated by experiments on Josephson junction arrays in a magnetic field and ultracold interacting atoms in an optical lattice in the presence of synthetic orbital magnetic fields, we study the "fully frustrated" Bose-Hubbard model and quantum XY model with half a flux quantum per lattice plaquette. Using Monte Carlo simulations and the density matrix renormalization group (DMRG) method, we show that the phase diagram of such kinetically frustrated bosons displays three phases on a two-leg ladder: a weakly interacting chiral superfluid phase with staggered loop currents which spontaneously break time-reversal symmetry, a conventional Mott insulator at strong coupling, and a remarkable "Chiral Mott Insulator" (CMI) with staggered loop currents sandwiched between them at intermediate correlation. We discuss how the CMI state may be viewed as an exciton condensate or a vortex supersolid, propose and study a Jastrow variational wavefunction which captures its correlations, present DMRG results for the boson momentum distribution across the phase diagram, and consider various experimental implications of our phase diagram. Finally, we discuss generalizations to a staggered flux Bose-Hubbard model and a two-dimensional version of the CMI with edge currents in weakly coupled ladders., Comment: 16 pages, 12 figures, Submitted to PRB; Short Rapid Comm paper is here -- http://arxiv.org/abs/1109.5703

We study a class of spin-1/2 quantum antiferromagnetic chains using DMRG technique. The exchange interaction in these models decreases linearly as a function of the separation between the spins, $J_{ij} = R-|i-j|$ for $|i-j| \le R$. For the separations beyond $R$, the interaction is zero. The range parameter $R$ takes positive integer values. The models corresponding to all the odd values of $R$ are known to have the same exact doubly degenerate dimer ground state as for the Majumdar-Ghosh (MG) model. In fact, R=3 is the MG model. For even $R$, the exact ground state is not known in general, except for R=2 (the Bethe ansatz solvable Heisenberg chain) and in the asymptotic limit of $R$ where the two MG dimer states again emerge as the exact ground state. In the present work, we numerically investigate the even-$R$ models whose ground state is not known analytically. In particular, for R=4, 6 and 8, we have computed a number of ground state properties. We find that, unlike R=2, the higher even-$R$ models are spin-gapped, and show strong dimer-dimer correlations of the MG type. Moreover, the spin-spin correlations decay very rapidly, albeit showing weak periodic revivals., Comment: 8 pages, 12 figures

In this paper we analyze the various phases exhibited by a system of ultracold bosons in a periodic optical superlattice using the mean field decoupling approximation. We investigate for a wide range of commensurate and incommensurate densities. We find the gapless superfluid phase, the gapped Mott insulator phase, and gapped insulator phases with distinct density wave orders., Comment: 6 pages, 7 figures, 4 tables

We develop an inhomogeneous mean-field theory for the extended Bose-Hubbard model with a quadratic, confining potential. In the absence of this potential, our mean-field theory yields the phase diagram of the homogeneous extended Bose-Hubbard model. This phase diagram shows a superfluid (SF) phase and lobes of Mott-insulator (MI), density-wave (DW), and supersolid (SS) phases in the plane of the chemical potential (\mu) and on-site repulsion (U); we present phase diagrams for representative values of V, the repulsive energy for bosons on nearest-neighbor sites. We demonstrate that, when the confining potential is present, superfluid and density-wave order parameters are nonuniform; in particular, we obtain, for a few representative values of parameters, spherical shells of SF, MI, DW, and SS phases. We explore the implications of our study for experiments on cold-atom dipolar condensates in optical lattices in a confining potential, Comment: Dedicated to Professor Ulrich Eckern on the occasion of his 60th birthday

We present an extensive study of Mott insulator (MI) and superfluid (SF) shells in Bose-Hubbard (BH) models for bosons in optical lattices with harmonic traps. For this we develop an inhomogeneous mean-field theory. Our results for the BH model with one type of spinless bosons agrees quantitatively with quantum Monte Carlo (QMC) simulations. Our approach is numerically less intensive than such simulations, so we are able to perform calculation on experimentally realistic, large 3D systems, explore a wide range of parameter values, and make direct contact with a variety of experimental measurements. We also generalize our inhomogeneous mean-field theory to study BH models with harmonic traps and (a) two species of bosons or (b) spin-1 bosons. With two species of bosons we obtain rich phase diagrams with a variety of SF and MI phases and associated shells, when we include a quadratic confining potential. For the spin-1 BH model we show, in a representative case, that the system can display alternating shells of polar SF and MI phases; and we make interesting predictions for experiments in such systems., Comment: 17 pages, 18 figures

We analyze various quantum phases of ultracold bosonic atoms in a periodic one dimensional optical superlattice. Our studies have been performed using the finite size density matrix renormalization group (FS-DMRG) method in the framework of the Bose-Hubbard model. Calculations have been carried out for a wide range of densities and the energy shifts due to the superlattice potential. At commensurate fillings, we find the Mott insulator and the superfluid phases as well as Mott insulators induced by the superlattice. At a particular incommensurate density, the system is found to be in the superfluid phase coexisting with density oscillations for a certain range of parameters of the system., Comment: 7 pages, 11 figures

We study a system of ultra-cold atoms possessing long range interaction (e.g. dipole-dipole interaction) in a one dimensional optical lattice in the presence of a confining harmonic trap. We have shown that for large enough on-site and nearest neighbor interaction a supersolid phase can be stabilized, consistent with the previous Quantum Monte Carlo and DMRG results for the homogeneous system. Due to the external harmonic trap potential the supersolid phase coexists with other phases. We emphasize on the experimental signatures of the various ground state phases in the presence of a trap., Comment: 9 pages, 16 figures

We report our findings on 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 yield the exotic supersolid phase where both the crystalline and the superfluid orders coexist. In addition, we obtain signatures for solitary waves and also superfluidity., Comment: 7 pages, 11 figures

It is well known that the supersolid form of matter can arise in a single species of cold bosonic atoms in an optical lattice due to long range interactions. We present a scenario where a supersolid is induced in one of the components of a mixture of two species bosonic atoms where there is no long range interactions. We study a system of normal and hardcore boson mixture with only the former possessing long range interactions. We consider three cases: the first where the total density is commensurate and the other two where they are incommensurate . By suitable choices of the densities and the interaction strengths of the atoms, we predict that the charge density wave and the supersolid orders can be induced in the hardcore species as a result of the competing interatomic interactions.

We study the Bose-Hubbard model using the finite size density matrix renormalization group method. We obtain for the first time a complete phase diagram for a system in the presence of a harmonic trap and compare it with that of the homogeneous system. To realize the transition from the superfluid to the Mott insulator phase we investigate different experimental signatures of these phases in quantities such as momentum distribution, visibility, condensate fraction and the total number of bosons at a particular density. The relationships between the various experimental signatures and the phase diagram are highlighted., Comment: 8 pages, 14 figures

We study the quantum phase transitions in a two component bose-mixture in a one-dimensional optical lattice. The calculations have been performed in the framework of the extended Bose-Hubbard model using the finite size density matrix renormalization group method. We obtain different phase transitions for the system for integer filling. When the inter-species on-site and the nearest neighbor interactions are larger than the intra-species on-site and also the nearest neighbor interactions, the system exhibits a phase separated charge density wave (PSCDW) order that is characterized by the two species being spatially separated and existing in the density wave phases.

We study a bosonic ladder with two coupled chains using the finite size density matrix renormalisation group method. We show that in a commensurate bosonic ladder the critical on-site interaction ($U_C$) for the superfluid to Mott insulator transition becomes larger as the inter-chain hopping ($t_\bot$)increases. We analyze this quantum phase transition and obtain the phase diagram in the $t_\bot -U$ plane., Comment: 6 pages, 10 figures

We generalize the mean-field theory for the spinless Bose-Hubbard model to account for the different types of superfluid phases that can arise in the spin-1 case. In particular, our mean-field theory can distinguish polar and ferromagnetic superfluids, Mott insulators which arise at integer fillings at zero temperature, and normal Bose liquids into which the Mott insulators evolve at finite temperatures. We find, in contrast to the spinless case, that several of the superfluid-Mott insulator transitions are first-order at finite temperatures. Our systematic study yields rich phase diagrams that include, first-order and second-order transitions, and a variety of tricritical points. We discuss the possibility of realizing such phase diagrams in experimental systems., Comment: 11 pages, 11 figures

We study the ground state quantum phase diagram for a two species Bose mixture in a one-dimensional optical lattice using the finite size density matrix renormalization group(FSDMRG) method. We discuss our results for different combinations of inter and intra species interaction strengths with commensurate and incommensurate fillings of the bosons. The phases we have obtained are superfluid, Mott insulator and a novel phase separation, where different species reside in spatially separate regions. The spatially separated phase is further classified into phase separated superfluid(PS-SF) and Mott insulator(PS-MI). The phase separation appears for all the fillings we have considered, whenever the inter-species interaction is slightly larger than the intra-species interactions., Comment: 7 pages, 7 figures

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 $\rho = 1$ in the $U-V$ 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 ($U, V) = (8.5 \pm 0.05, 4.75 \pm 0.05)$., Comment: 10 pages, 15 figures

We use the density matrix renormalization group to study the quantum transitions that occur in the half-filled one-dimensional fermionic Hubbard model with onsite potential disorder. We find a transition from the gapped Mott phase with algebraic spin correlations to a gapless spin-disordered phase beyond a critical strength of the disorder $\Delta_c \approx U/2$. Both the transitions in the charge and spin sectors are shown to be coincident. We also establish the finite-size corrections to the charge gap and the spin-spin correlation length in the presence of disorder and using a finite-size-scaling analysis we obtain the zero temperature phase diagram of the various quantum phase transitions that occur in the disorder-interaction plane., Comment: 4 RevTeX pages with 6 EPSF figures included via psfig