Temperature evolution of the quantum gap in CsNiCl3 - art. no. 134417

Neutron-scattering measurements on the one-dimensional gapped S = 1 antifer romagnet, CsNiCl3, have shown that excitation corresponding to the Haldane mass gap Delta at low temperatures persists as a resonant feature to high t emperatures. We find that the strong upward renormalization of the gap exci tation, by a factor of three between 5 and 70 K, is more than enough to ove rcome its decreasing lifetime. We find that the gap lifetime is substantial ly shorter than that predicted by the scaling theory of Damle and Sachdev b ased on a classical dispersion for the Haldane excitations, but when we inc lude their expected relativistic dispersion, the theory, in its low-tempera ture range of validity, gives a good account of experiment. The upward gap renormalization agrees with the nonlinear sigma model at low temperatures a nd even up to T of order 2 Delta provided an upper momentum cutoff is inclu ded.