Dual fermion approach to nonlocal correlations in the Hubbard model

TL;DR

The paper introduces a dual fermion diagrammatic technique for accurately capturing nonlocal correlations in the Hubbard model, effectively bridging weak and strong coupling regimes and reproducing pseudogap phenomena with minimal diagrams.

Contribution

It develops a novel dual fermion approach that simplifies the treatment of nonlocal effects in Hubbard-like models, improving upon cluster methods.

Findings

Successfully reproduces antiferromagnetic pseudogap formation.

Provides an efficient interpolation between weak-coupling and atomic limits.

Treats irreducible vertices as small parameters for simplified calculations.

Abstract

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.