• Accepted Paper

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

Ivan Jakovac, Mihael S. Grbić, Maxime Dupont, Nicolas Laflorencie, Sylvain Capponi, Yuko Hosokoshi, Steffen Krämer, Yurii Skourski, Sven Luther, Masashi Takigawa, and Mladen Horvatić

Phys. Rev. Lett. - Accepted 28 July, 2026

DOI: https://doi.org/10.1103/89k5-p261

Abstract

We present a comprehensive low-temperature 1H nuclear magnetic resonance (NMR) study of magnetic field-induced phases and spin fluctuations in an isotropic Haldane chain system m-NO2PhBNO (BoNO) in fields up to 34~T. NMR spectral and T11 relaxation rate data are used to map out the transition temperature Tc(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 Tc(B)(BBc2)ν with ν=2/3 and universal quasiparticle scaling in the low-temperature limit close to Bc2. The extensive Bayesian inference analysis of the temperature and field dependence of T11(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.

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