Tomonaga-Luttinger liquid and quantum criticality in spin- $\frac{1}{2}$ antiferromagnetic Heisenberg chain C ₁₄ H ₁₈ CuN ₄ O ₁₀ via Wilson ratio

The ground state of a one-dimensional spin- $\frac{1}{2}$ uniform antiferromagnetic Heisenberg chain (AfHc) is a Tomonaga-Luttinger liquid which is quantum-critical with respect to applied magnetic fields up to a saturation field ${\mu }_0{H}_s$ beyond which it transforms to a fully polarized state. Wilson ratio has been predicted to be a good indicator for demarcating these phases [Phys. Rev. B 96, 220401 (2017)]. From detailed temperature and magnetic field-dependent magnetization, magnetic susceptibility and specific heat measurements in a metalorganic complex and comparisons with field theory and quantum transfer matrix method calculations, the complex was found to be a very good realization of a spin- $\frac{1}{2}$ AfHc. Wilson ratio obtained from experimentally obtained magnetic susceptibility and magnetic contribution of specific heat values was used to map the magnetic phase diagram of the uniform spin- $\frac{1}{2}$ AfHc over large regions of phase space demarcating Tomonaga-Luttinger liquid, saturation field quantum critical, and fully polarized states. Luttinger parameter and spinon velocity were found to match very well with the values predicted from conformal field theory.