Heisenberg-antiferromagnet and loop-soup

An analytic approximation to the loop-soup approach of Liang et al. to the spin 1/2 Heisenberg antiferromagnet is introduced. It allows for a staggered long-range correlation of the spins ind>1 dimensions. The wavevector-dependence for the static spin-correlation function and for the averaged spinwave-energy agrees qualitatively with that obtained in spinwave approximation. Since my approximation does not exclude the intersection of loops, the expectation value of the spin-spin correlation at short distances is larger by a factor of approximately 3/2, similarly as in the Boson mean-field approximation. The elementary bosonic excitations of this theory correspond in my case to single unpaired spins moving on one sublattice through the system with (apart from a different overall prefactor) the same dispersion. Within the present approach the amplitudesh of the singlets in the wave function fall off liker ^–d–1 for pairs of spins a distancer apart, if long-range order is present. This suggests that the loop-soup picture may be a good starting point for further investigations.Work supported in part by the Deutsche Forschungsgemeinschaft through Sonderforschungsbereich 123 Stochastic Mathematical Models