Mean-field approaches to the Bose–Hubbard model with three-body local interaction

The zero temperature properties of the generalized Bose–Hubbard model including three-body interactions are studied on a mean-field level. We obtain analytical results using the so-called perturbative mean-field method and more detailed numerical results using the Gutzwiller product state variational ansatz. These two approaches yield equivalent results which compare well on a qualitative level with recent exact results obtained in the literature. (paper)