Quantum-critical spin dynamics in a Tomonaga-Luttinger liquid studied with muon-spin relaxation

We demonstrate that quantum-critical spin dynamics can be probed in high magnetic fields using muon-spin relaxation ($mu^{+}$SR). Our model system is the strong-leg spin ladder bis(2,3-dimethylpyridinium) tetrabromocuprate (DIMPY). In the gapless Tomonaga-Luttinger liquid phase we observe finite-temperature scaling of the $mu^{+}$SR $1/T_1$ relaxation rate which allows us to determine the Luttinger parameter $K$. We discuss the benefits and limitations of local probes compared with inelastic neutron scattering.