One-loop approximation for the Heisenberg antiferromagnet
  We use the diagram technique for spin operators to calculate Green's functions and observables of the spin-1/2 quantum Heisenberg antiferromagnet on a square lattice. The first corrections to the self-energy and interaction are taken into account in the chain diagrams. The approximation reproduces main results of Takahashi's modified spin-wave theory [Phys. Rev. B 40, 2494 (1989)] and is applicable in a wider temperature range. The energy per spin calculated in this approximation is in good agreement with the Monte Carlo and small-cluster exact-diagonalization calculations in the range 0 <= T < 1.2J where J is the exchange constant. For the static uniform susceptibility the agreement is good for T < 0.6J and becomes somewhat worse for higher temperatures. Nevertheless the approximation is able to reproduce the maximum in the temperature dependence of the susceptibility near T = 0.9J. 
A. Sherman and M. Schreiber