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

The low-energy physics of anti ferromagnets 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 = (pi/2a, +/-pi/2a). 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. (c) 2007 Elsevier B.V. All rights reserved.