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.