Longitudinal excitations in triangular lattice antiferromagnets

TL;DR

This paper investigates the longitudinal excitation spectra of quantum antiferromagnets on a triangular lattice using a microscopic many-body approach, revealing gapless behavior at certain points and discussing potential additional modes.

Contribution

It introduces a detailed calculation of longitudinal excitation spectra for the triangular lattice antiferromagnet, including the possibility of a second longitudinal mode due to noncollinear order.

Findings

Longitudinal modes become gapless at specific points in the Brillouin zone.

Finite-size effects or anisotropy induce a large energy gap in these modes.

Potential existence of a second longitudinal mode due to noncollinear magnetic order.

Abstract

We study the longitudinal excitations of quantum antiferromagnets on a triangular lattice by a recently proposed microscopic many-body approach based on magnon-density waves. We calculate the full longitudinal excitation spectra of the antiferromagnetic Heisenberg model for a general spin quantum number in the isotropic limit. Similar to the square lattice model, we find that, at the center of the first hexagonal Brillouin zone $\Gamma(\mathbf q=0)$ and at the magnetic ordering wavevectors $\pm[\mathbf Q= (4\pi/3,0)]$, the excitation spectra become gapless in the thermodynamic limit, due to the slow, logarithmic divergence of the structure factor. However, these longitudinal modes on two-dimensional models may be considered as quasi-gapped, as any finite-size effect or small anisotropy will induce a large energy gap, when compared with the counterpart of the transverse spin-wave excitations. We also discuss a possible second longitudinal mode in the triangular lattice model due to the noncollinear nature of its magnetic order.