Magnon damping in the two-dimensional quantum Heisenberg antiferromagnet at short wavelengths.

Abstract

Dyson-Maleev boson formalism is used to calculate magnon damping ${\mathrm{\ensuremath{\Gamma}}}_{\mathbf{k}}$ in the two-dimensional quantum Heisenberg antiferromagnet at low temperatures T and for wavelengths short compared to the thermal de Broglie wavelength. From the evaluation of the second-order self-energy it is found that ${\mathrm{\ensuremath{\Gamma}}}_{\mathbf{k}}$\ensuremath{\propto}${\mathit{T}}^{3}$Z(\ensuremath{\Vert}${\mathbf{v}}_{\mathbf{k}}$\ensuremath{\Vert}) as T\ensuremath{\rightarrow}0, where ${\mathbf{v}}_{\mathbf{k}}$ is the gradient of dispersion relation of free magnons. For k close to the boundary of the Brillouin zone, where \ensuremath{\Vert}${\mathbf{v}}_{\mathbf{k}}$\ensuremath{\Vert} is small, the function Z has the expansion Z(\ensuremath{\Vert}${\mathbf{v}}_{\mathbf{k}}$\ensuremath{\Vert})=1+O(\ensuremath{\Vert}${\mathbf{v}}_{\mathbf{k}}$${\mathrm{\ensuremath{\Vert}}}^{2}$). For general \ensuremath{\Vert}${\mathbf{v}}_{\mathbf{k}}$\ensuremath{\Vert}, we have calculated Z numerically. Although there is no long-range order at any T\ensuremath{\ne}0, the staggered correlation length \ensuremath{\xi}(T) is exponentially large as T\ensuremath{\rightarrow}0. It is shown explicitly in the present work that, at low temperatures, magnons with momentum k in the regime \ensuremath{\Vert}k\ensuremath{\Vert}a\ensuremath{\gg}(T/${\mathit{E}}_{\mathrm{\ensuremath{\pi}}}$${)}^{1/3}$ (where a is the lattice spacing and ${\mathit{E}}_{\mathrm{\ensuremath{\pi}}}$ is the energy of zone-boundary magnons) are well-defined quasiparticles. We present evidence to support the argument that this remains true as long as \ensuremath{\Vert}k\ensuremath{\Vert}\ensuremath{\xi}\ensuremath{\gg}1.