Breakdown of the conventional spin-wave dynamics and its double-constraint modification in the spin-$\mathbf{\frac{1}{2}}$ triangular-prism Heisenberg antiferromagnet

TL;DR

This paper investigates magnon decay dynamics in a frustrated spin-1/2 triangular prism antiferromagnet, revealing a novel instability and proposing a double-constraint modification to conventional spin-wave theory to address infrared divergence and anharmonicities.

Contribution

It introduces a double-constraint modification to spin-wave theory that overcomes limitations of traditional approaches in noncollinear, frustrated antiferromagnets.

Findings

Identifies a novel instability in the single-particle spectrum.

Shows conventional spin-wave theory fails to handle anharmonicities.

Proposes a double-constraint approach to accurately describe nonlinear spin-wave dynamics.

Abstract

Spontaneous magnon decays in an $S=\frac{1}{2}$ 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.