Spin waves in a triangular lattice antiferromagnet: Decays, spectrum renormalization, and singularities

We present a comprehensive study of the dynamical properties of the quantum Heisenberg antiferromagnet on a triangular lattice within the framework of spin-wave theory. The distinct features of spin-wave excitations in the triangular lattice antiferromagnet are (i) finite lifetime at zero temperature due to spontaneous two-magnon decays, (ii) strong renormalization of magnon energies ε_k with respect to the harmonic result, and (iii) logarithmic singularities in the decay rate Γ_k. Quantum corrections to the magnon spectrum are obtained using both the on-shell and off-shell solutions of the Dyson equation with the lowest-order magnon self-energy. At low-energies magnon excitations remain well defined albeit with the anomalous decay rate Γ_k∝k² at k→0 and Γ_k∝|k−Q_AF|^7/2 at k→Q_AF. At high energies, magnons are heavily damped with the decay rate reaching (2Γ_k/ε_k)∼0.3 for the case S=1/2. The on-shell solution shows logarithmic singularities in Γ_k with the concomitant jumplike discontinuities in Re[ε_k] along certain contours in the momentum space. Such singularities are even more prominent in the magnon spectral function A(k,ω). Although the off-shell solution removes such log singularities, the decay rates remain strongly enhanced. We also discuss the role of higher-order corrections and show that such singularities may lead to complete disappearance of the spectrum in the vicinity of certain k points. The kinematic conditions for two-magnon decays are analyzed for various generalizations of the triangular lattice antiferromagnet as well as for the XXZ model on a kagomé lattice. Our results suggest that decays and singularities in the spin-wave spectra must be ubiquitous in all these systems. In addition, we give a detailed introduction in the spin-wave formalism for noncollinear Heisenberg antiferromagnets and calculate several quantities for the triangular lattice model including the ground-state energy and the sublattice magnetization.