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Physical Review B

Momentum distribution of the hard-core extended boson Hubbard model in one dimension

Min-Chul Cha, Jong-Geun Shin, Ji-Woo Lee

Published Nov 17, 2009• 6 citations
Publisher

Abstract

We investigate the momentum distribution associated with quantum phase transitions between a superfluid and a charge-density-wave state in the one-dimensional hard-core extended boson Hubbard model at half filling by using the Lanczos exact diagonalization method. The momentum distribution shows distinct features in different regions. At the Heisenberg point, it shows a universal behavior. In the superfluid phase, the Luttinger-liquid parameters are easily obtained from the finite-size scaling behaviors of the zero-momentum occupancy. Also the signature of a charge-density wave can be identified in the insulating phase.

DOI
10.1103/physrevb.80.193104

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We investigate the momentum distribution associated with quantum phase transitions between a superfluid and a charge-density-wave state in the one-dimensional hard-core extended boson Hubbard model at half filling by using the Lanczos exact diagonalization method. The momentum distribution shows distinct features in different regions. At the Heisenberg point, it shows a universal behavior. In the superfluid phase, the Luttinger-liquid parameters are easily obtained from the finite-size scaling behaviors of the zero-momentum occupancy. Also the signature of a charge-density wave can be identified in the insulating phase.
We study a model for interacting spinless bosons in one dimension. The bosons are under a hard-core condition, which does not allow two or more bosons in the same site. However, nearestneighbor interactions between bosons ( V ) and hoppings to the nearest empty site ( t ) are allowed. As V increases from a large negative value, the system undergoes a quantum phase transition from a phase-separation (PS) phase to a superfluid (SF) phase because the hopping term overcomes the attractive energy. When V becomes positive and is increased more, the superfluid phase becomes a charge-density-wave (CDW) phase because the repulsive energy blocks the movements of bosons. Via exact diagonalizations, we calculated the ground-state energies, the correlation energies, and the kinetic energies to obtain signatures of the quantum phase transitions. We adopted a fast stateseeking algorithm that enabled us to calculate the ground states and the ground-state energies up to L = 32 more efficiently. Some results are compared with those of quantum Monte Carlo simulations by using stochastic series expansion for the Heisenberg point, and the momentum distribution functions for the three phases are discussed.
We study quantum phase transitions in a hard-core boson model with nearest-neighbor repulsions in one dimension. As we change the repulsive energy, V , between bosons occupying nearest neighbors, the model exhibits a quantum phase transition from a superfluid (SF) to a charge-density-wave (CDW)-type solid phase at half-filling. By using an exact diagonalization method with a modified Lanczos method, we calculate the ground-state energies up to a precision of O (10 −7 ). From the ground-state energies, we obtain the number of dimers by taking numerical derivatives of the groundstate energies. Because the dissolution of the dimers occurs because of the repulsive energy, V , we find a signature of the quantum phase transition from the behaviors of the correlation energy and those of the number of dimers as a function of V .
We study a model for two-species hard-core bosons in one dimension. In this model, the same-species bosons have a hard-core condition at the same site, while different-species bosons are allowed to occupy the same site with a local interaction U . At half-filling, by Jordan-Wigner transformation, the model can be exactly mapped to a fermionic Hubbard model. Due to this correspondence, the phase transition from superfluid ( U = 0) to Mott insulator ( U > 0) can be explained by simple one-band theory at half-filling. By using an exact diagonalization method adopting a modified Lanczos method, we obtain the ground states as a function of U for the lattice size upto L = 16. We calculate directional current-current correlation functions in this model, which indicate that there are some remaining counter-flow in the Mott insulating region ( U > 0) and co-flow in the charge-density-wave region ( U <0) for the finite lattices.
We use quantum Monte Carlo simulations and exact diagonalization to explore the phase diagram of the Bose-Hubbard model with an additional superlattice potential. We first analyze the properties of superfluid and insulating phases present in the hard-core limit where an exact analytic treatment is possible via the Jordan-Wigner transformation. The extension to finite on-site interactions is achieved by means of quantum Monte Carlo simulations. We determine insulator and superfluid phase diagrams as functions of the on-site repulsive interaction, superlattice potential strength, and filling, finding that insulators with fractional occupation numbers, which are present in the hard-core case, extend deep into the soft-core region. Furthermore, at integer fillings, we find that the competition between the on-site repulsion and the superlattice potential can produce a phase transition between a Mott insulator and a charge-density-wave insulator, with an intermediate superfluid phase. Our results are relevant to the behavior of ultracold atoms in optical superlattices which are beginning to be studied experimentally.
We have obtained the quantum phase diagram of one dimensional extended Bose-Hubbard model using the density-matrix renormalization group and Abelian bosonization methods for different commensurabilities. We describe the nature of different quantum phases at the charge degeneracy point. We find a direct phase transition from Mott insulating phase to superconducting phase for integer band fillings of bosons. We predict explicitly the presence of two kinds of repulsive Luttinger liquid phases, apart from the charge density wave and superconducting phases for half-integer band fillings. Our study reveals that extended range interactions are necessary to get the correct phase boundary of an one-dimensional interacting bosons system.