Broken symmetry in antiferromagnets

Abstract

We discuss limitations of the conventional 'broken symmetry' picture of the Heisenberg antiferromagnet. The exact results on the ground state of the linear chain and of the three-dimensional Hamiltonian do not show a 'degeneracy of the vacuum'. With the help of a solvable model it is shown that the correlations in the ground state may have the Neel character, as revealed by the neutron experiments, even though the ground state is quite different from the Neel states. There is no Goldstone mode in the linear chain. The spin of the antiferromagnetic spin wave is 1/2. But the physical states have a doublet of the spin waves which could be regarded as degenerate states of spin 1 and spin 0. The fermionic character is suppressed and the bosonic character revealed, as in the decolouring phenomena in quantum field theory. It is plausible that in the three-dimensional case also there is no Goldstone mode.