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We determine the ground-state properties of a gas of interacting bosonicatoms in a one-dimensional optical lattice. The system is modelled by theBose-Hubbard Hamiltonian. We show how to apply the time-evolving blockdecimation method to systems with periodic boundary conditions, and employ itas a reference to find the ground state of the Bose-Hubbard model. Results arecompared with recently proposed approximate methods, such asHartree-Fock-Bogoliubov (HFB) theories generalised for strong interactions andthe variational Bijl-Dingle-Jastrow method. We find that all HFB methods do notbring any improvement to the Bogoliubov theory and therefore provide correctresults only in the weakly-interacting limit, where the system is deeply in thesuperfluid regime. On the other hand, the variational Bijl-Dingle-Jastrowmethod is applicable for much stronger interactions, but is essentially limitedto the superfluid regime as it reproduces the superfluid-Mott insulatortransition only qualitatively.

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