Wilson ratio of a Tomonaga-Luttinger liquid in the one-dimensional spin-$1/2$ Heisenberg antiferromagnet CuPzN

In the Tomonaga-Luttinger liquid (TLL) phase of a one-dimensional antiferromagnet, the Wilson ratio and the TLL parameter, $K$, are one and the same except for a trivial numerical factor. This equivalence allows the determination of $K$ from magnetic susceptibility and specific heat. We have performed accurate magnetization and specific-heat measurements on the quasi-one-dimensional spin-1/2 Heisenberg antiferromagnet Cu(C$_4$H$_4$N$_2$)(NO$_3$)$_2$, known as CuPzN, at temperatures between 80 mK and 7.5 K and in magnetic fields up to 14.7 T and, from the data in the TLL regime, have obtained $K$ as a function of the magnetic field. The results are in excellent agreement with a prediction based on the Bethe ansatz.