Once one admits the electronic state is described by the molecular-orbitals (MOs), the system has flat bands when the number of MOs is less than the total number of atoms. Then it is natural the electron-electron interaction is also given by the interaction between the MO electrons. In this case, correlation functions of this correlated system (gapped filled flat band) are obtained simply by using Wick’s theorem. In one dimension, its correlation length is analytically obtained as well. Look at our paper, “Construction of interacting flat-band models by molecular-orbital representation: Correlation functions, energy gap, and entanglement” by Tomonari Mizoguchi, Yoshihito Kuno, Yasuhiro Hatsugai, Progress of Theoretical and Experimental Physics, Volume 2022, Issue 2, 023I02 (2022) Published: 28 January 2022.