Finite-temperature correlations in a quantum spin chain near saturation

Inelastic neutron-scattering and finite-temperature density matrix renormalization group (DMRG) calculations are used to investigate the spin excitation spectrum of the $S=1/2$ Heisenberg spin chain compound ${\mathrm{K}}_{2}{\mathrm{CuSO}}_{4}{\mathrm{Cl}}_{2}$ at several temperatures in a magnetic field near saturation. Critical correlations characteristic of the predicted $z=2,\phantom{\rule{0.16em}{0ex}}d=1$ quantum phase transition occurring at saturation are shown to be consistent with the observed neutron spectra. The data is well described with a scaling function computed using a free fermion description of the spins, valid close to saturation, and the corresponding scaling limits. One of the most prominent nonuniversal spectral features of the data is a novel thermally activated longitudinal mode that remains underdamped across most of the Brillouin zone.