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 (C$_{7}$H$_{10}$N)$_{2}$CuBr$_{4}$ 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 $K\approx1.25$ and scaling function are in excellent agreement with density matrix renormalization group numerical calculations for the underlying spin Hamiltonian. 
K. Yu. Povarov, D. Schmidiger, N. Reynolds, R. Bewley, A. Zheludev
cond-mat.str-el