Total energy method based on the density functional theory (DFT) is the cornerstone of current theory of real materials. Almost all basic properties of materials can be derived from the total energy and its derivatives with respect to physical variables. Meanwhile, there are interesting phenomena that DFT cannot cover, to name a few, incommensurate orders in crystals, twisted two-dimensional lattices, and thermodynamics of them, simply because the systems include too many atoms. Applying the total energy method to huge systems while keeping the accuracy is one of the greatest challenges in computational materials physics.

In this talk, I will introduce my interatomic potential approach which is capable of handling millions of atoms with DFT-level-accuracy. Using the approach, I tackled three problems; (1) multiple charge density wave (CDW) phase transitions in two-dimensional crystal 2H-TaSe₂, (2) missing soft phonon problem in kagome metal (CsV₃Sb₅) during the CDW phase transition, and (3) the full phase diagram of twisted trilayer graphene. “Computer experiments” including millions of atoms reproduce the real experimental results and careful investigation of the simulations reveals the physics behind. In the order listed above, we have found that the structural origins of incommensurate CDWs, preformation of CDW, and the crucial role of a long-range interlayer interaction in graphene. Implications of them on other materials will be also discussed.