Systematic low-energy effective theory for magnons and charge carriers in an antiferromagnet

Abstract

By electron or hole doping quantum antiferromagnets may turn into high-temperature superconductors. The low-energy dynamics of antiferromagnets are governed by their Nambu–Goldstone bosons—the magnons—and are described by an effective field theory analogous to chiral perturbation theory for the pions in strong interaction physics. In analogy to baryon chiral perturbation theory—the effective theory for pions and nucleons—we construct a systematic low-energy effective theory for magnons and electrons or holes in an antiferromagnet. The effective theory is universal and makes model-independent predictions for the entire class of antiferromagnetic cuprates. We present a detailed analysis of the symmetries of the Hubbard model and discuss how these symmetries manifest themselves in the effective theory. A complete set of linearly independent leading contributions to the effective action is constructed. The coupling to external electromagnetic fields is also investigated.