SPIN-WAVES IN QUANTUM ANTIFERROMAGNETS

Using a self-consistent mean-field theory for the S=1/2 Heisenberg ant iferromagnet, Kruger and Schuck recently derived an analytic expressio n for the dispersion. It is exact in one dimension (d = 1) and agrees well with numerical results in d = 2. With an expansion in powers of t he inverse coordination number 1/Z (Z = 2d) we investigate if this exp ression can be exact for all d. The projection method of Mori-Zwanzig is used for the dynamical spin susceptibility. We find that the expres sion of Kruger and Schuck deviates in order 1/Z(2) from our rigorous r esult. Our method is generalized to arbitrary spin S and to models wit h easy-axis anisotropy Delta. It can be systematically improved to hig her orders in 1/Z. We clarify its relation to the 1/S expansion.