Tomonaga–Luttinger liquid and quantum criticality in spin-12 antiferromagnetic Heisenberg chain <i>C</i>14<i>H</i>18<i>CuN</i>4<i>O</i>10 via Wilson ratio

The ground state of a one-dimensional spin- <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow><mml:mfrac><mml:mn>1</mml:mn> <mml:mrow><mml:mn>2</mml:mn></mml:mrow> </mml:mfrac> </mml:mrow> </mml:math> 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 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>μ</mml:mi> <mml:mn>0</mml:mn></mml:msub> <mml:msub><mml:mi>H</mml:mi> <mml:mi>s</mml:mi></mml:msub> </mml:math> 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- <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow><mml:mfrac><mml:mn>1</mml:mn> <mml:mrow><mml:mn>2</mml:mn></mml:mrow> </mml:mfrac> </mml:mrow> </mml:math> 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- <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow><mml:mfrac><mml:mn>1</mml:mn> <mml:mrow><mml:mn>2</mml:mn></mml:mrow> </mml:mfrac> </mml:mrow> </mml:math> 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.