Entanglement and heat capacity in a two-atom Bose-Hubbard model

► Entanglement sudden transitions are found in non-trivial exactly solvable Hubbard models. ► Entanglement and heat capacity exhibit three anti-correlated phases. ► Qualitative changes of thermal entanglement or heat capacity occur at critical points. ► We propose thermodynamical measurements to single out entanglement critical points.