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

Fund: Stimulating discussions with Shuai Chen, Donna Sheng, Jan Zaanen, and Jia-Xin Zhang are acknowledged. A partial support of this work by the National Key R&D Program of China (Grant No. 2017YFA0302902) is also acknowledged.

Jing-Yu Zhao(赵靖宇) and Zheng-Yu Weng(翁征宇) Mottness, phase string, and high-T_{c} superconductivity 2022 Chin. Phys. B 31 087104

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