In contrast to hole-doped systems which have hole pockets centered at (± π 2a , ± π 2a ), in lightly electron-doped antiferromagnets the charged quasiparticles reside in momentum space pockets centered at ( π a , 0) or (0, π a ). This has important consequences for the corresponding low-energy effective field theory of magnons and electrons which is constructed in this paper. In particular, in contrast to the hole-doped case, the magnonmediated forces between two electrons depend on the total momentum P of the pair. For P = 0 the one-magnon exchange potential between two electrons at distance r is proportional to 1/r 4 , while in the hole case it has a 1/r 2 dependence. The effective theory predicts that spiral phases are absent in electron-doped antiferromagnets.

The long-range forces between holes in an antiferromagnet are due to magnon exchange. The one-magnon exchange potential between two holes is proportional to cos(2ϕ)/ r 2 where r is the distance vector of the holes and ϕ is the angle between r and an axis of the square crystal lattice. One-magnon exchange leads to bound states of holes with antiparallel spins resembling d-wave symmetry. The role of these bound states as potential candidates for the preformed Cooper pairs of high-temperature superconductivity is discussed qualitatively.

Identifying the correct low-energy effective theory for magnons and holes in an antiferromagnet has remained an open problem for a long time. In analogy to the effective theory for pions and nucleons in QCD, based on a symmetry analysis of Hubbard and t-J-type models, we construct a systematic low-energy effective field theory for magnons and holes located inside pockets centered at lattice momenta (±). The effective theory is based on a nonlinear realization of the spontaneously broken spin symmetry and makes model-independent universal predictions for the entire class of lightly doped antiferromagnetic precursors of high-temperature superconductors. The predictions of the effective theory are exact, order by order in a systematic low-energy expansion. We derive the one-magnon exchange potentials between two holes in an otherwise undoped system. Remarkably, in some cases the corresponding two-hole Schrödinger equations can even be solved analytically. The resulting bound states have d-wave characteristics. The ground state wave function of two holes residing in different hole pockets has a d x 2 −y 2 -like symmetry, while for two holes in the same pocket the symmetry resembles d xy .

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 2a , ± π 2a ). Even though the symmetries are extracted from the Hubbard model, the effective theory is universal and makes modelindependent 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.

We have constructed a systematic low-energy effective theory for hole-and electron-doped antiferromagnets, where holes reside in momentum space pockets centered at (± π 2a , ± π 2a ) and where electrons live in pockets centered at ( π a , 0) or (0, π a ). The effective theory is used to investigate the magnon-mediated binding between two holes or two electrons in an otherwise undoped system. We derive the one-magnon exchange potential from the effective theory and then solve the corresponding two-quasiparticle Schrödinger equation. As a result, we find bound state wave functions that resemble d x 2 −y 2 -like or dxy-like symmetry. We also study possible ground states of lightly doped antiferromagnets.