Electron correlations in a Hubbard antiferromagnetic semiconductor. Weak coupling

Matrix Dyson equation for the Hubbard model is obtained by the method of irreducible Green's functions. The self-energy operator is expressed in terms of the highorder irreducible Green's function, which is calculated approximately in the weak binding case $U\ll W$, where $U$ is the interatomic repulsion and $W$ – the half band width. This approximation corresponds to the dressing of the electrons by the boson collective excitations: fluctuations of the spin and electron density of two-electron clusters with opposite spins. In the Hartree–Fock approximation (HFA) a system with one electron per atom is an antiferromagnetic semiconductor. The correlation effects lead to magnetopolaron narrowing of the energy gap. It is shown that such an antiferromagnetic state exists with the arbitrarily small interaction, as well as in the HFA.