Mottness, phase string, and high-T _c superconductivity

It is a great discovery in physics of the twentieth century that elementary particles Nature are dictated by gauge forces, characterized nonintegrable phase factor an particle charge $q$ acquires from A to B points: $$P \exp\left(i\frac{q}{\hbar c} \int_A^B A_\mu dx^\mu\right)$$ where $A_\mu$ potential and $P$ stands for path ordering. In many-body system strongly correlated electrons, if so-called Mott gap opened up interaction, corresponding Hilbert space will be fundamentally changed. novel known as phase-string appear replace conventional Fermi statistics dictate low-lying physics. Protected gap, which clearly identified high-$T_c$ cuprate with magnitude > 1.5 eV, such singular can enforce fractionalization leading dual world exotic topological structure. non-Fermi-liquid "parent" state emerge, gapless Landau quasiparticle only partially robust around arc regions, while main dynamics dominated two types gapped spinons. Antiferromagnetism, superconductivity, liquid full surface regarded low-temperature instabilities this new parent state. Both numerics experiments provide direct evidence emergent Mottness, lies core superconducting mechanism.