Abstract:
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.