Generalized Effective Potential Landau Theory for Bosonic Quadratic Superlattices

We study the properties of the Bose-Hubbard model for a quadratic optical superlattice. To this end we generalize a recently established effective potential Landau theory for a single component to the case of multi components and find not only the characteristic incompressible solid phases with fractional filling, but also obtain the underlying quantum phase diagram in the whole parameter region at zero temperature. Comparing our analytic results with corresponding ones from quantum Monte Carlo simulations demonstrates the high accuracy of the generalized effective potential Landau theory (GEPLT). Finally, we comment on the advantages and disadvantages of the GEPLT in view of a direct comparison with a corresponding decoupled mean-field theory.