A new diagrammatic technique is developed to describe nonlocal effects (e.g., pseudogap formation) in the Hubbard-like models. In contrast to cluster approaches, this method utilizes an exact transition to the dual set of variables, and it therefore becomes possible to treat the irreducible vertices of an effective {\it single-impurity} problem as small parameters. This provides a very efficient interpolation between weak-coupling (band) and atomic limits. The antiferromagnetic pseudogap formation in the Hubbard model is correctly reproduced by just the lowest-order diagrams.
@article{arxiv.cond-mat/0612196,
title = {Dual fermion approach to nonlocal correlations in the Hubbard model},
author = {A. N. Rubtsov and M. I. Katsnelson and A. I. Lichtenstein},
journal= {arXiv preprint arXiv:cond-mat/0612196},
year = {2007}
}