Temperature dependence of the NMR relaxation rate 1/T_1 for quantum spin chains

TL;DR

This paper uses tensor network simulations to study how the NMR relaxation rate 1/T_1 varies with temperature in quantum spin chains, bridging classical diffusive and Tomonaga-Luttinger liquid regimes for better experimental interpretation.

Contribution

It provides a numerical analysis of 1/T_1 in spin chains across temperature regimes, comparing tensor network results with analytical TLL predictions for the first time.

Findings

Quantitative limits on TLL theory validity range.

Identification of crossover behavior in spin chains.

Application to realistic material models like DTN.

Abstract

We present results of numerical simulations performed on one-dimensional spin chains in order to extract the so-called relaxation rate $1/T_1$ accessible through NMR experiments. Building on numerical tensor network methods using the Matrix Product States (MPS) formalism, we can follow the non-trivial 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-$1/2$ XXZ chain which is a paradigm of gapless TLL, as well as a more realistic spin-$1$ anisotropic chain, modelling 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.