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Electronic States and Anomalous Hall Effect in Strongly Correlated Topological Systems

We treat elementary excitations, the spin-liquid state, and the anomalous Hall effect (including the quantum one in purely 2D situation) in layered highly correlated systems. The mechanisms of the formation of a topological state associated with bare flat energy bands, correlations, and spin-orbit interactions, including the appearance of correlated Chern bands, are analyzed. A two-band picture of the spectrum in metallic kagome lattices is proposed, which involves a transition from the ferromagnetic state, a flat strongly correlated band, and a band of light Dirac electrons. In this case, the effect of separation of the spin and charge degrees of freedom turns out to be significant. The application of the representations of the Kotliar-Rukenstein auxiliary bosons and the Ribeiro-Wen dopons to this problem is discussed.