Analysis and resolution of the ground-state degeneracy of the two-component Bose-Hubbard model

We study the degeneracy of the ground-state energy E of the two-component Bose-Hubbard model and of the perturbative correction E-1. We show that the degeneracy properties of E and E-1 are closely related to the connectivity properties of the lattice. We determine general conditions under which E is nondegenerate. This analysis is then extended to investigate the degeneracy of E-1. In this case, in addition to the lattice structure, the degeneracy also depends on the number of particles present in the system. After identifying the cases in which E-1 is degenerate and observing that the standard (degenerate) perturbation theory is not applicable, we develop a method to determine the zeroth-order correction to the ground state by exploiting the symmetry properties of the lattice. This method is used to implement the perturbative approach to the two-component Bose-Hubbard model in the case of degenerate E-1 and is expected to be a valid tool to perturbatively study the asymmetric character of the Mott insulator to superfluid transition between the particle and hole side.