# NMR relaxation in the spin-1 Heisenberg chain

## TL;DR

This paper investigates the dynamical properties of the spin-1 Heisenberg chain at finite temperature, focusing on NMR relaxation rates, revealing spin diffusion at high temperatures and activated behavior at very low temperatures.

## Contribution

It provides a detailed numerical analysis of the NMR relaxation rate in the spin-1 Heisenberg chain, highlighting temperature-dependent behaviors near the Haldane gap.

## Key findings

- Spin diffusion observed at high temperatures.
- Activated behavior only at temperatures much lower than the gap.
- Analysis of contributions from modes near q≈0 and q≈π.

## Abstract

We consider the isotropic $S=1$ Heisenberg chain with a finite Haldane gap $\Delta$ and use state-of-the-art numerical techniques to investigate its dynamical properties at finite temperature, focusing on the nuclear spin-lattice relaxation rate $1/T_1$ measured in nuclear magnetic resonance (NMR) experiments for instance. In particular, we analyze the contributions from modes with momenta close to $q\approx 0$ and $q\approx \pi$ as a function of temperature. At high-temperature, we observe spin diffusion with a non-trivial exponent. At low-temperature, we argue that a simple activated behavior $1/T_1 \propto\exp(-\Delta/T)$ can only be observed at temperatures much smaller than the gap $\Delta$.