From the Hubbard model to a systematic low-energy effective field theory for magnons and holes in an antiferromagnet

Abstract

The low-energy physics of antiferromagnets is governed by their Goldstone bosons – the magnons – and it is described by a low-energy effective field theory. In analogy to baryon chiral perturbation theory, we construct the effective field theory for magnons and holes in an antiferromagnet. It is a systematic low-energy expansion based on symmetry considerations and on the fact that the holes are located in pockets centered at k = ( π 2 a , ± π 2 a ) . Even though the symmetries are extracted from the Hubbard model, the effective theory is universal and makes model-independent predictions about the dynamical mechanisms in the antiferromagnetic phase. The low-energy effective theory has been used to investigate one-magnon exchange which leads to a d-wave-shaped bound state of holes.