Model quantum magnet. II. Calculation of NMR line shapes

Abstract

Following an earlier lead in which we had demonstrated the role of the hyperfine interaction in both the phase diagram and the dynamic susceptibility for a model quantum magnet such as LiHoF₄, we calculate the NMR line shape in this system. Although the nuclear quadrupolar component of the interaction is tiny compared to the strength of the (dipolar) hyperfine interaction, the former turns out to be a crucial diagnostic tool, especially near the quantum critical point. We have carried out both a stochastic treatment and an ab initio many-body calculation in order to have complementary insight into the algebraic expressions as well as the computed NMR spectra. We hope our derived results will motivate NMR experiments on the quantum critical phenomena in LiHoF₄.