One-particle dynamics in the Hubbard model at half-filling

Abstract

The one-particle Green function for the 2d Hubbard model at half-filling and zero temperature is considered. By use of projection technique we derive equations of motion for the Green functions related to the four Hubbard operators c ̂ kσ α and c ̂ kσ α . Here, the index α = 1, 2indicates the two sublattices of the antiferromagnetic phase. The operator c ̂ kσ α creates a hole on sublattice α at singly occupied sites. Similarly, c ̂ kσ α annihilates an electron at doubly occupied sites. The self-energy matrix is decoupled and a self-consisten scheme for the Green functions is found. This scheme can be considered a generalization of one derived recently for the t- J model. For the hole band, described by the operators c ̂ kσ α , our result for U⪢ t shows strong coupling of the hole to spin excitations, similar to that found for the t- j model, with the additional feature that propagation of up-spin holes on the down sublattice is taken into account. For decreasing U the gap decreases roughly proportional to the staggered magnetization m. For U → 0, where m vanishes, we find the correct limit of uncorrelated electrons.