Scaling of temporal correlations in an attractive Tomonaga-Luttinger spin liquid

We report temperature-dependent neutron scattering measurements of the local dynamic structure factor in the quantum spin ladder (C7H10N)2CuBr4 in a magnetic field H = 9 T, in its gapless quantum-critical phase. We show that the measured quantity has a scaling form consistent with expectations for a Tomonaga-Luttinger liquid with attraction. The measured Luttinger parameter K ≈ 1.25 and scaling function are in excellent agreement with density matrix renormalization group numerical calculations for the underlying spin Hamiltonian.