Magnetic-Field-Induced Tomonaga-Luttinger Liquid and Bose-Einstein Condensate Phases in an Organic S=1 Haldane Chain.

We present a comprehensive low-temperature ^{1}H nuclear magnetic resonance (NMR) study of magnetic field-induced phases and spin fluctuations in an isotropic Haldane chain system m-NO_{2}PhBNO (BoNO) in fields up to 34 T. NMR spectral and T_{1}^{-1} relaxation rate data are used to map out the transition temperature T_{c}(B) and we show that it defines a complete phase boundary between the field-induced Bose-Einstein condensate (BEC) and Tomonaga-Luttinger liquid (TLL) phases by reproducing its shape via quantum Monte Carlo calculations. We also observe the theoretical critical behavior T_{c}(B)∝(B-B_{c2})^{ν} with ν=2/3 and universal quasiparticle scaling in the low-temperature limit close to B_{c2}. The extensive Bayesian inference analysis of the temperature and field dependence of T_{1}^{-1}(T,B) reveals attractive interactions across the TLL phase of a Haldane chain. Our results are further corroborated by magnetostriction measurements in pulsed magnetic fields and density matrix renormalization group calculations.