Magnetic-field-induced Tomonaga-Luttinger liquid and Bose-Einstein condensate phases in an organic S=1 Haldane chain

Abstract

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 $T_c(B)\propto (B-B_{\text{c2}}{)}^{\nu }$ with $\nu =2/3$ and universal quasiparticle scaling in the low-temperature limit close to $B_{\text{c2}}$. 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.

arXiv comment9 pages, 3 figures