Abstract
Using the diagrammatic technique for Hubbard operators we construct a linked-cluster perturbation expansion around the atomic limit of the Hubbard model. We first perform a computer-aided fourth-order calculation. The results clarify discrepances in earlier expansions around the large-U limit. Next, we construct a partial vertex renormalization in the second order of the linked-cluster expansion. The vertex renormalization leads to a selfconsistent magnetic symmetry breaking and allows to study explicitly magnetic oderings of the system in the whole range of temperatures and for arbitrary electron density. The presented results for the case of a half-filled energy band indicate that our approach for the Hubbard model is analogous to the mean-field theory for spin systems, and can serve as a starting point for developing advanced selfconsistent schemes which become exact in the large-U limit. We present results of a systematic numerical study of the non-half-filled-band case. In particular, the vertex-renormalized second-order calculation leads to a qualitatively correct sharp decrease of the Néel temperature as a function of concentration of holes.
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