$z=2$ Quantum Critical Dynamics in a Spin Ladder

By means of inelastic neutron scattering we investigate finite temperature dynamics in the quantum spin ladder compound (C${}_5$H${}_{12}$N)${}_2$CuBr${}_4$ (BPCB) near the magnetic field induced quantum critical point with dynamical exponent $z=2$. We observe universal finite-temperature scaling of the transverse local dynamic structure factor in spectacular quantitative agreement with long-standing theoretical predictions. At the same time, already at rather low temperatures, we observe strong non-universal longitudinal fluctuations. To separate the two, we make use of an intrinsic leg-exchange symmetry of the spin ladder. Complementary measurements of specific heat also reveal striking scaling behavior near the quantum critical point.