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.