Electrons in solids are in motion within the energy band reflecting the lattice structure of each material. The Coulomb interaction, electron-lattice interaction, and spin-orbit interaction have nontrivial effects on the motion of electrons and induce various interesting phenomena. Our aim is to elucidate the emergent quantum phenomena induced by cooperation or competition of these interactions, using state-of-the-art computational methods for condensed matter physics. Our current focus is on various functional transition metal oxides, topological materials, and heterostructures made of these materials. Our research will lead not only to clarify the mechanism of quantum phenomena in existent materials but also to propose novel materials.