We present the dynamical spin structure factor of the antiferromagnetic spin-$\frac{1}{2} J_1\text{−}{J}_2$ Heisenberg model on a triangular lattice obtained from large-scale matrix-product state simulations. The high frustration due to the combination of antiferromagnetic nearest- and next-nearest-neighbor interactions yields a rich phase diagram. We resolve the low-energy excitations both in the ${120}^{\circ }$ ordered phase and in the putative spin-liquid phase at $J_2/J_1=0.125$. In the ordered phase, we observe an avoided decay of the lowest magnon branch, demonstrating the robustness of this phenomenon in the presence of gapless excitations. Our findings in the spin-liquid phase chime with the field-theoretical predictions for a gapless Dirac spin liquid, in particular the picture of low-lying monopole excitations at the corners of the Brillouin zone. We comment on possible practical difficulties of distinguishing proximate liquid and solid phases based on the dynamical structure factor.

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• Magnons
• Quantum spin liquid
• Spin dynamics
• Triangular lattice
• Density matrix renormalization group
• Matrix product states