The Bose-Hubbard ground state: extended Bogoliubov and variational methods compared with time-evolving block decimation

Abstract

We determine the ground-state properties of a gas of interacting bosonic atoms in a one-dimensional optical lattice. The system is modelled by the Bose-Hubbard Hamiltonian. We show how to apply the time-evolving block decimation method to systems with periodic boundary conditions, and employ it as a reference to find the ground state of the Bose-Hubbard model. Results are compared with recently proposed approximate methods, such as Hartree-Fock-Bogoliubov (HFB) theories generalised for strong interactions and the variational Bijl-Dingle-Jastrow method. We find that all HFB methods do not bring any improvement to the Bogoliubov theory and therefore provide correct results only in the weakly-interacting limit, where the system is deeply in the superfluid regime. On the other hand, the variational Bijl-Dingle-Jastrow method is applicable for much stronger interactions, but is essentially limited to the superfluid regime as it reproduces the superfluid-Mott insulator transition only qualitatively.

9 pages, 8 figures

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• Superfluid to Mott insulator transition in the one-dimensional Bose-Hubbard model for arbitrary integer filling factors
• Quantum phase slips in one-dimensional superfluids in a periodic potential
• Semiclassical quench dynamics of Bose gases in optical lattices
• Accurate numerical verification of the instanton method for macroscopic quantum tunneling: dynamics of phase slips
• Quantum phase transition of Bose-Einstein condensates on a ring nonlinear lattice
• End-to-end entanglement in Bose-Hubbard chains
• Quasiequilibrium Mixture of Itinerant and Localized Bose Atoms in Optical Lattice
• Noise correlations of one-dimensional Bose mixtures in optical lattices
• Quantum damping of Fermi-Pasta-Ulam revivals in ultracold Bose gases
• Critical temperature of noninteracting bosonic gases in cubic optical lattices at arbitrary integer fillings
• Phase Transitions in Three-Dimensional Bosonic Systems in Optical Lattices
• A Quantum Theory of Cold Bosonic Atoms in Optical Lattices
• Mode folding in systems with local interaction: unitary and non-unitary transformations using tensor states
• Quantum Effects In Low Temperature Bosonic Systems
• A quantum phase transition in a quantum external field: Superposing two magnetic phases