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 current carriers, is treated. application this to spin-liquid, antiferromagnetic nearly systems proposed with use various bosonic fermionic representations, a comparison perturbation in $s-d(f)$ exchange model being performed. The topological aspects including formation small Fermi surface are In case narrow bands (strong correlations), ground considered as direct product RVB dopon or Weng's fermion states. Examples Kondo lattices, doped pyrochlores, $\beta$-Mn, YMn$_2$, Y$_{1-x}$Sc$_x$Mn$_2$ discussed, analogies copper-oxide