NMR relaxation rates for the spin-1/2 Heisenberg chain

TL;DR

This paper calculates NMR relaxation rates for the spin-1/2 Heisenberg chain using quantum Monte Carlo and compares results with analytical predictions, revealing the influence of hyperfine form factors on temperature-dependent behavior.

Contribution

It provides numerical calculations of relaxation rates and analyzes how hyperfine form factors affect the temperature dependence in the Heisenberg chain.

Findings

Low-temperature behavior extends up to T/J ≈ 0.5 for peaked hyperfine form factors.

Significant weight at q ≈ 0 introduces diffusive processes requiring lower temperatures.

Asymptotic T→0 forms are observable only at very low temperatures for broad form factors.

Abstract

The spin-lattice relaxation rate $1/T_1$ and the spin echo decay rate $1/T_{2G}$ for the spin-$1\over 2$ antiferromagnetic Heisenberg chain are calculated using quantum Monte Carlo and maximum entropy analytic continuation. The results are compared with recent analytical calculations by Sachdev. If the nuclear hyperfine form factor $A_q$ is strongly peaked around $q=\pi$ the predicted low-temperature behavior [$1/T_1 \sim \ln{^{1/2}(1/T)}$, $1/T_{2G} \sim \ln{^{1/2}(1/T)}/\sqrt{T}$] extends up to temperatures as high as $T/J \approx 0.5$. If $A_q$ has significant weight for $q \approx 0$ there are large contributions from diffusive long-wavelength processes not taken into account in the theory, and very low temperatures are needed in order to observe the asymptotic $T \to 0$ forms.