During recent years, the study of T=0 quantum phase transitions (QPT), the emergent scaling properties and their profound influence on physical properties at T>0 has attracted a lot of interest, ranging from metal-insulator transitions, Bose-Einstein condensation to various field- or pressure-driven QPTs of quantum magnets. We propose to study the QPT and the exotic zero-scale universality of a 1D Heisenberg spin chain material in the vicinity of the field-induced QPT between the gapless Luttinger Liquid and gapped polarized state. Surprisingly, this type of quantum critical point has not been addressed in detail so far and only few thermodynamic and NMR studies exist. Inelastic neutron scattering, however, is the optimal method in order to study this QCP since it allows us to directly access the scaling properties of the time- and space-dependent spin-spin correlation function.