Entanglement and heat capacity in a two-atom Bose\u2013Hubbard model

We show that a two-atom Bose\u2013Hubbard model exhibits three different phases in the behavior of thermal entanglement in its parameter space. These phases are demonstrated to be traceable back to the existence of level crossings in the ground state of the same system. Significant similarities between the behaviors of thermal entanglement and heat capacity in the parameter space are brought to light thus allowing to interpret the occurrence and the meaning of all these three phases