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Two-band model and RVB-type states: application to Kondo lattices, pyrochlores and Mn-based systems

An exotic fractionalized Fermi-liquid FL$^*$ theory of metallic systems, which combines resonant-valence-bond (RVB) state and the band of current carriers, is treated. An application of this theory to spin-liquid, antiferromagnetic and nearly antiferromagnetic systems is proposed with the use of various bosonic and fermionic representations, a comparison with perturbation theory in the $s-d(f)$ exchange model being performed. The topological aspects including formation of the small Fermi surface are treated. In the case of narrow bands (strong correlations), the ground state is considered as a direct product of RVB and dopon or Weng's fermion states. Examples of Kondo lattices, doped pyrochlores, and metallic $β$-Mn, YMn$_2$, Y$_{1-x}$Sc$_x$Mn$_2$ systems are discussed, analogies with copper-oxide systems being treated.