Designing novel quantum materials for quantum technology is one of challenging topics of modern condensed matter physics. To attain the desired functionalities of complex systems, understanding of how the different physical degrees of freedom such as charge, spin, orbital, and lattice, tune the properties of materials is a first step. The long term goal of our research is to achieve theoretical principles of emergent phenomena in complex quantum materials. We consider the delicate balance among charge, spin, lattice and orbital degrees of freedom, and their interplay which lead to rich physics. Examples that we study include spin liquids, topological insulators, topological metals, topological superconductors, high temperature superconductors, electronic liquid crystalline materials, frustrated quantum magnets, ultra-cold atom systems, thermoelectric materials, and transition metal oxide superlattices.