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Combining inelastic neutron scattering and numerical simulations, we studythe quasi-one dimensional Ising anisotropic quantum antiferromagnet \bacovo\ ina longitudinal magnetic field. This material shows a quantum phase transitionfrom a N\'eel ordered phase at zero field to a longitudinal incommensurate spindensity wave at a critical magnetic field of 3.8 T. Concomitantly theexcitation gap almost closes and a fundamental reconfiguration of the spindynamics occurs. These experimental results are well described by the universalTomonaga-Luttinger liquid theory developed for interacting spinless fermions inone dimension. We especially observe the rise of mainly longitudinalexcitations, a hallmark of the unconventional low-field regime in Ising-likequantum antiferromagnet chains.

Tomonaga-Luttinger liquid spin dynamics in the quasi-one dimensional Ising-like antiferromagnet BaCo$_2$V$_2$O$_8$