From the Hubbard Model to a Systematic Low-Energy Effective Field Theory for Magnons and Holes in an Antiferromagnet

TL;DR

This paper develops a systematic low-energy effective field theory for magnons and holes in antiferromagnets, based on symmetry principles, enabling model-independent predictions about their interactions and bound states.

Contribution

It introduces a universal effective field theory for magnons and holes in antiferromagnets, inspired by baryon chiral perturbation theory, extending the understanding of low-energy excitations.

Findings

Derived a systematic low-energy expansion based on symmetry.

Predicted a d-wave-shaped bound state of holes due to magnon exchange.

Established the universality of the effective theory independent of microscopic details.

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=(pi/2a,\pm 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.