Self-Consistent Spin-Wave Approach to the Quantum Antiferromagnet on a Triangular Lattice

Abstract

The self-consistent spin-wave approach proposed in the previous paper is applied to the XY and Heisenberg antiferromagnets with S=1⁄2 on a triangular lattice. Our approach is composed of two procedures. One is that the approximate boson representation of spin operators is derived from the equations of motion linearized about the equilibrium state on the assumption of the appearance of a long-range order (LRO). The other is that the following constraint is retained in the average: (S_j^y)²+(S_j^z)²=1⁄2 when the x-axis is taken as the quantized one. Our estimates for the LRO and ground-state energy are in fairly good agreement with the results obtained by various methods. In contrast with the ordinary spin-wave theories, it is emphasized that the constraint becomes more effective in the systems with large spin fluctuations due to the zero-point motion.