Spin diffusion and the anisotropic spin-1/2 Heisenberg chain

TL;DR

This paper investigates spin diffusion in the one-dimensional Heisenberg antiferromagnet Sr_2CuO_3, showing diffusion-like behavior at high temperatures that diminishes exponentially at low temperatures, linking it to free fermion models.

Contribution

It provides a detailed analysis of spin diffusion contributions in the anisotropic spin-1/2 Heisenberg chain using density-matrix renormalization group data, clarifying temperature-dependent behavior.

Findings

Diffusion-like contribution exists for T > J

Exponential suppression of diffusion at T << J

Frequency dependence connects to free fermion case

Abstract

Measurements of the spin-lattice relaxation rate 1/T_1 by nuclear magnetic resonance for the one-dimensional Heisenberg antiferromagnet Sr_2CuO_3 have provided evidence for a diffusion-like contribution at finite temperature and small wave-vector. By analyzing real-time data for the auto- and nearest-neighbor spin-spin correlation functions obtained by the density-matrix renormalization group I show that such a contribution indeed exists for temperatures T>J, where J is the coupling constant, but that it becomes exponentially suppressed for T << J. I present evidence that the frequency-dependence of 1/T_1 in the Heisenberg case is smoothly connected to that in the free fermion case where the exponential suppression of the diffusion-like contribution is easily understood.