  The space- and time-dependent response of many-body quantum systems is the
most informative aspect of their emergent behaviour. The dynamical structure
factor, experimentally measurable using neutron scattering, can map this
response in wavevector and energy with great detail, allowing theories to be
quantitatively tested to high accuracy. Here, we present a comparison between
neutron scattering measurements on the one-dimensional spin-1/2 Heisenberg
antiferromagnet KCuF3, and recent state-of-the-art theoretical methods based on
integrability and density matrix renormalization group simulations. The
unprecedented quantitative agreement shows that precise descriptions of
strongly correlated states at all distance, time and temperature scales are now
possible, and highlights the need to apply these novel techniques to other
problems in low-dimensional magnetism.
