Generalized effective-potential Landau theory for a tunable state-dependent hexagonal optical lattice

We analytically study the ground-state phase diagrams of ultracold bosons with various effective magnetic quantum number m in a state-dependent hexagonal optical lattice by using the generalized effective-potential Landau theory. While the first-order results correspond to mean field approximation, our third-order analytical results are in excellent agreement with the previous cluster Gutzwiller solutions. Furthermore, we reveal the reason why the regions of the Mott lobes (n,n) in phase diagrams for m=0.02 are unexpectedly expanded with increasing J/U in deep lattice. Besides, at the tips of the Mott lobes, the critical values Jc/U have also been obtained analytically as functions of the site-offset energy ϵ/U. Comparing the results obtained by our third-order analytical calculations and previous numerical solutions, we find that the relative deviations are less than 9% (5%) for Mott insulator with (half-)integer filling.