Two-dimensional Heisenberg antiferromagnets play a central role in quantum magnetism, yet the nature of dynamic correlations in these systems at finite temperature has remained poorly understood for decades. We solve this long-standing problem by using a novel quantum-classical duality to calculate the dynamic structure factor analytically and, paradoxically, find a broad frequency spectrum despite the very long quasiparticle lifetime. The solution reveals new multi-scale physics whereby an external probe creates a classical radiation field containing infinitely-many quanta. Crucially, it is the multi-scale nature of this phenomenon which prevents a conventional renormalization group approach. We also challenge the common wisdom on static correlations and perform Monte Carlo simulations which demonstrate excellent agreement with our theory.
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