  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.
