Mott localization nurtures several competing and coexisting orders

Band insulating diamond or metallic mercury differs in a fundamental fashion from materials containing Mott localized electrons. Proliferation of long range orders that compete and sometimes coexist is an important consequence of Mott localization. In this article we focus on how Mott localization creates a rich phase diagram and new physics. A projected nature of the low energy Hilbert space, as opposed to a Fermi gas like Hilbert space, underlies this. Spin, orbital and charge degree of freedom gain independence, but get quantum entangled among themselves and create novel phases. We focus on spin-half single orbital systems. Mott localization encourages entanglement of spin pairs via valence bond formation. We relate valence bond dynamics to emergent gauge fields. Emergent gauge fields in turn nurture and encourage a variety of orders, including topological orders: antiferromagnetism, spin liquids, charge, spin stripes, chiral order and robust superconducting order.