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arXiv:0905.1027 · Physical Review A

Momentum distribution of the insulating phases of the extended Bose-Hubbard model

M. Iskin, James K. Freericks

Published Dec 4, 2009• 20 citations
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Abstract

We develop two methods to calculate the momentum distribution of the insulating (Mott and charge-density-wave) phases of the extended Bose-Hubbard model with on-site and nearest-neighbor boson-boson repulsions on $d$-dimensional hypercubic lattices. First, we construct the random-phase approximation result, which corresponds to the exact solution for the infinite-dimensional limit. Then, we perform a power-series expansion in the hopping $t$ via strong-coupling perturbation theory, to evaluate the momentum distribution in two and three dimensions; we also use the strong-coupling theory to verify the random-phase approximation solution in infinite dimensions. Finally, we briefly discuss possible implications of our results in the context of ultracold dipolar Bose gases with dipole-dipole interactions loaded into optical lattices.

DOI
10.1103/physreva.80.063610

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We develop two methods to calculate the momentum distribution of the insulating (Mott and charge-density-wave) phases of the extended Bose-Hubbard model with on-site and nearest-neighbor boson-boson repulsions on ddd-dimensional hypercubic lattices. First, we construct the random-phase approximation result, which corresponds to the exact solution for the infinite-dimensional limit. Then, we perform a power-series expansion in the hopping ttt via strong-coupling perturbation theory, to evaluate the momentum distribution in two and three dimensions; we also use the strong-coupling theory to verify the random-phase approximation solution in infinite dimensions. Finally, we briefly discuss possible implications of our results in the context of ultracold dipolar Bose gases with dipole-dipole interactions loaded into optical lattices.
We develop a strong-coupling perturbation theory for the extended Bose-Hubbard model with on-site and nearest-neighbor boson-boson repulsions on (d>1)(d>1)(d>1)-dimensional hypercubic lattices. Analytical expressions for the ground-state phase boundaries between the incompressible (Mott or charge-density-wave insulators) and the compressible (superfluid or supersolid) phases are derived up to third order in the hopping ttt. We also briefly discuss possible implications of our results in the context of ultracold dipolar Bose gases with dipole-dipole interactions loaded into optical lattices.
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To analyze the ground-state phase diagram of Bose-Bose mixtures loaded into ddd-dimensional hypercubic optical lattices, we perform a strong-coupling power-series expansion in the kinetic energy term (plus a scaling analysis) for the two-species Bose-Hubbard model with onsite boson-boson interactions. We consider both repulsive and attractive interspecies interaction, and obtain an analytical expression for the phase boundary between the incompressible Mott insulator and the compressible superfluid phase up to third order in the hoppings. In particular, we find a re-entrant quantum phase transition from paired superfluid (superfluidity of composite bosons, i.e., Bose-Bose pairs) to Mott insulator and again to a paired superfluid in all one, two, and three dimensions, when the interspecies interaction is sufficiently large and attractive. We hope that some of our results could be tested with ultracold atomic systems.
We use the Gutzwiller ansatz and analyze the phase diagram of the extended Bose-Hubbard Hamiltonian with on-site (UUU) and nearest-neighbor (VVV) repulsions. For ddd-dimensional hypercubic lattices, when 2dV<U2\mathit{dV}<U2dV<U, it is well known that the ground state alternates between the charge-density-wave (CDW) and Mott insulators, and the supersolid (SS) phase occupies small regions around the CDW insulators. However, when 2dV>U2\mathit{dV}>U2dV>U, in this Rapid Communication, we show that the ground state has only CDW insulators, and more importantly, the SS phase occupies a much larger region in the phase diagram, existing up to very large hopping values which could be orders of magnitude higher than that of the well-known case. In particular, the SS-superfluid phase boundary increases linearly as a function of hopping when $2\mathit{dV}\ensuremath{\gtrsim}1.5U$, for which the prospects of observing the SS phase with dipolar Bose gases loaded into optical lattices is much higher.
We present a strong-coupling expansion of the Bose-Hubbard model which describes both the superfluid and the Mott phases of ultracold bosonic atoms in an optical lattice. By performing two successive Hubbard-Stratonovich transformations of the intersite hopping term, we derive an effective action which provides a suitable starting point to study the strong-coupling limit of the Bose-Hubbard model. This action can be analyzed by taking into account Gaussian fluctuations about the mean-field approximation as in the Bogoliubov theory of the weakly interacting Bose gas. In the Mott phase, we reproduce results of previous mean-field theories and also calculate the momentum distribution function. In the superfluid phase, we find a gapless spectrum and compare our results with the Bogoliubov theory.
For systems of interacting, ultracold spin-zero neutral bosonic atoms, harmonically trapped and subject to an optical lattice potential, we derive an Extended Bose Hubbard (EBH) model by developing a systematic expansion for the Hamiltonian of the system in powers of the lattice parameters and of a scale parameter, the lattice attenuation factor. We identify the dominant terms that need to be retained in realistic experimental conditions, up to nearest-neighbor interactions and nearest-neighbor hoppings conditioned by the on-site occupation numbers. In the mean field approximation, we determine the free energy of the system and study the phase diagram both at zero and at finite temperature. At variance with the standard on site Bose Hubbard model, the zero-temperature phase diagram of the EBH model possesses a dual structure in the Mott insulating regime. Namely, for specific ranges of the lattice parameters, a density wave phase characterizes the system at integer fillings, with domains of alternating mean occupation numbers that are the atomic counterparts of the domains of staggered magnetizations in an antiferromagnetic phase. We show as well that in the EBH model, a zero-temperature quantum phase transition to pair superfluidity is, in principle, possible, but completely suppressed at the lowest order in the lattice attenuation factor. Finally, we determine the possible occurrence of the different phases as a function of the experimentally controllable lattice parameters.