Decoding flat bands from compact localized states

The flat band system is an ideal quantum platform to investigate the kaleidoscope created by the electron-electron correlation effects. The central ingredient of realizing a flat band is to find its compact localized states. In this work, we develop a systematic way to generate the compact localized states by designing destructive interference pattern from 1-dimensional chains. A variety of 2-dimensional new flat band systems are constructed with this method. Furthermore, we show that the method can be extended to generate the compact localized states in multi-orbital systems by carefully designing the block hopping scheme, as well as in quasicrystal and disorder systems.