Temperature dependence of the NMR relaxation rate 1 /T1 for quantum spin chains

We present results of numerical simulations performed on one-dimensional spin chains in order to extract the so-called relaxation rate 1 /T₁ accessible through NMR experiments. Building on numerical tensor network methods using the matrix product states formalism, we can follow the nontrivial crossover occurring in critical chains between the high-temperature diffusive classical regime and the low-temperature response described by the Tomonaga-Luttinger liquid (TLL) theory, for which analytical expressions are known. In order to compare analytics and numerics, we focus on a generic spin-1 /2 X X Z chain which is a paradigm of gapless TLL, as well as a more realistic spin-1 anisotropic chain, modeling the DTN material, which can be either in a trivial gapped phase or in a TLL regime induced by an external magnetic field. Thus, by monitoring the finite temperature crossover, we provide quantitative limits on the range of validity of TLL theory, that will be useful when interpreting experiments on quasi-one-dimensional materials.