Strong coupling Hartree-Fock approximation in the dynamical mean-field theory

In the limit of infinite spatial dimensions a thermodynamically consistent theory, which is valid for arbitrary value of the Coulombic interaction (U < ∞), is built for the Hubbard model when the total auxiliary single-site problem exactly splits into four subspaces with different “vacuum states”. Some analytical results are given for the Hartree-Fock approximation when the 4-pole structure for Green’s function is obtained: two poles describe contribution from the Fermi liquid component, which is ferromagnetic and dominant for small electron and hole concentrations (“overdoped case” of high-Tc’s), whereas other two describe contribution from the non-Fermi liquid, which is antiferromagnetic and dominant close to half filling (“underdoped case”).