Formation of exotic states in the $s-d$ exchange and $t-J$ models

Different scenarios of the implementation of the two-band model in systems of strongly correlated electrons, including frustrated magnetic systems, high-temperature superconductors, and Kondo lattices, are considered. The interaction of current carriers with magnetic moments in the representations of pseudofermions or Schwinger bosons describing the spinon excitations is studied on the basis of the derived Hamiltonians of the $s-d$ exchange and $t-J$ models within the formalism of many-electron Hubbard $X$ operators.