By carefully controlling the competing parameters of strong electronic correlation U, spin-orbit coupling factor λ, intriguing quantum phases can be achieved including Mott insulator, topological insulator, Weyl semimetal and Kitaev Materials. Many of them have special topological behavior and those who have invariant property under topological transformation was called topological materials. The most famous topological materials are called topological insulators whose bulk is insulating while conducting in the surface.
Another novel phenomena induced by strong electronic correlation was called Quantum Spin Liquid (QSL) state. Unlike conventional magnetic states, a QSL state is a fluid-like magnetic state which never enters into a long-range ordered phase, even at absolute zero temperature. Many exotic behavior was expected due to this special frustrated behavior, for example, the existence of spinons and the absence of phase transition when lowering down the temperature. The ideal QSL state should possess a high degree of quantum entanglement with fractionalized quantum excitations. Just like room temperature superconducting, it has been a long argue since Anderson's notion of QSL more than four decades ago but still yet to be answered: "Do quantum spin liquid exist?"

Theoretically there are many proposed possible model and structures to realise QSL, most of which are based on triangular-bansed lattice structure, for example, triangular or Kagome lattice. Among them, a special group called Kitaev model has got special attention because it have two different source of frustration with both ferromagnetic and antiferromagnetic interaction between transition metal oxide sites. So far there have been many promising experimental results but the "smoking-gun" characterization method for QSL is still a mystery.
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2D electronic liquids
Superconductivity exotic magnetic and orbital states
Topological matter with strong correlations: AHE QSL Kitaev