Mutually attracting spin waves in the square-lattice quantum antiferromagnet

Spin waves (magnons) in two dimensions are the potential glue in high-temperature superconductors so that their quantitative understanding is mandatory. Yet even for the fundamental case of the undoped Heisenberg model on the square lattice a consistent picture is still lacking. Significant spectral continua are taken as evidence of the existence of fractional excitations (spinons), but descriptions in terms of spinons fail to show the established absence of an energy gap. Here a fully consistent picture of the dynamics in the square-lattice quantum antiferromagnet is provided which agrees with the experimental findings. The key step is to capture (i) the strong attractive interaction between the spin waves and (ii) the vertex corrections of the observables.