Correlation function in interacting flat-band models constructed by molecular-orbital representation

We calculate correlation functions of exactly-solvable one-dimensional flat-band models by utilizing the molecular-orbital representation. The models considered in this paper have a gapped ground state with flat-band being fully occupied, even in the presence of the interaction. The remarkable feature of such models is that the correlation functions are obtained without deriving explicit forms of the flat-band wave functions. Rather, they can be calculated by using the molecular-orbitals. As a demonstration, several one-dimensional models and their correlation functions are presented.