  We present a 13C-NMR study of the magnetic field driven transition to
complete polarization of the S=1/2 antiferromagnetic Heisenberg chain system
copper pyrazine dinitrate Cu(C_4H_4N_2)(NO_3)_2 (CuPzN). The static local
magnetization as well as the low-frequency spin dynamics, probed via the
nuclear spin-lattice relaxation rate 1/T_1, were explored from the low to the
high field limit and at temperatures from the quantum regime (k_B T << J) up to
the classical regime (k_B T >> J). The experimental data show very good
agreement with quantum Monte Carlo calculations over the complete range of
parameters investigated. Close to the critical field, as derived from static
experiments, a pronounced maximum in 1/T_1 is found which we interpret as the
finite-temperature manifestation of a diverging density of zero-energy magnetic
excitations at the field-driven quantum critical point.
