Temperature effects on superfluid phase transition in Bose–Hubbard model with three-body interaction

•We study the Mott–superfluid transition in the Bose–Hubbard model.•Three-body interactions are taken into account.•New method based on the resolvent of the statistical sum is used.•We calculate the effect of temperature on the phase diagram.

We theoretically investigate the effect of the three-body on-site interactions on the Mott-insulator–superfluid transition for ultracold bosonic atoms in the framework of the Bose–Hubbard model. In particular, we explore the combined effects of three-body interaction and finite temperature on the phase diagram in detail. In order to handle system with strong local interactions a resolvent expansion technique based on the contour integral representation of the partition function has been devised. Subsequently, we derive the Landau-type expansion for the free energy in terms of the superfluid order parameter and find the phase diagrams depicting the relationships between various physical quantities of interest.