Spontaneous magnon decays in an S= 12 Heisenberg antiferromagnet on the equilateral triangular prism are investigated in terms of modified magnon Green's functions. In one dimension, the so-called infrared divergence prevents us from calculating any —whether static or dynamic— structure factor within the conventional spin-wave theory even at zero temperature. The well-known modified spin-wave theory initiated by Takahashi completely fails to treat anharmonicities to cause transverse-to-longitudinal coupling which are quite characteristic of noncollinear antiferromagnets. We propose imposing a double-constraint condition on spin waves to solve all these difficulties and get a full view of the nonlinear spin-wave dynamics in one-dimensional frustrated noncollinear antiferromagnets. We reveal a novel instability of the single-particle spectrum in the absence of any well-defined magnetically ordered ground state.
Yamamoto et al. (Thu,) studied this question.