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 an
d 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.
We report comprehensive inelastic neutron scattering measurements of the magnetic excitations in the 2D spin-5/2 Heisenberg antiferromagnet Rb2MnF4 as a function of temperature from deep in the Neel ordered phase up to paramagnetic, 0.13 < kBT/4JS <
1.4. Well defined spin-waves are found for wave-vectors larger than the inverse correlation length $eta^{-1}$ for temperatures up to near the Curie-Weiss temperature, $Theta_{CW}$. For wave-vectors smaller than $eta^{-1}$, relaxational dynamics occurs. The observed renormalization of spin-wave energies, and evolution of excitation line-shapes, with increasing temperature are quantitatively compared with finite-temperature spin-wave theory, and computer simulations for classical spins. Random phase approximation calculations provide a good description of the low-temperature renormalisation of spin-waves. In contrast, lifetime broadening calculated using the first Born approximation shows, at best, modest agreement around the zone boundary at low temperatures. Classical dynamics simulations using an appropriate quantum-classical correspondence were found to provide a good description of the intermediate- and high-temperature regimes over all wave-vector and energy scales, and the crossover from quantum to classical dynamics observed around $Theta_{CW}/S$, where the spin S=5/2. A characterisation of the data over the whole wave-vector/energy/temperature parameter space is given. In this, $T^2$ behaviour is found to dominate the wave-vector and temperature dependence of the line widths over a large parameter range, and no evidence of hydrodynamic behaviour or dynamical scaling behaviour found within the accuracy of the data sets.
