Hydrodynamic spin fluctuations in the antiferromagnetic Heisenberg chain

TL;DR

This paper investigates the finite-temperature spin dynamics of the antiferromagnetic Heisenberg chain, revealing a transition from propagating spinons to diffusive spin transport, and characterizing this behavior through quantum Monte Carlo and other methods.

Contribution

It provides a detailed analysis of the dynamic structure factor and spin transport properties, including the spin-current relaxation rate, using quantum Monte Carlo and finite-size scaling techniques.

Findings

Transition from spinon propagation to diffusion at small momentum

Quantitative characterization of spin-current relaxation rate versus temperature and magnetic field

Consistency with Bethe Ansatz, exact diagonalization, and previous theoretical approaches

Abstract

We study the finite temperature, low energy, long wave-length spectrum of the dynamic structure factor of the spin-$1/2$ antiferromagnetic Heisenberg chain in the presence of exchange anisotropy and external magnetic fields. Using imaginary-time quantum Monte-Carlo we extract parameters, relevant to characterize a {\it renormalized} Luttinger liquid. For small momentum our results are consistent with a change from propagating spinon density waves to spin diffusion, described by a finite-frequency spin-current relaxation rate. Results for this relaxation rate as well as other Luttinger liquid parameters are presented versus temperature, momentum, magnetic field, and anisotropy, including finite-size analysis, and checks for anomalous diffusion. Our results are consistent with exact diagonalization and Bethe Ansatz, where available, and with corroborate findings of other previous studies using bosonization, transfer matrix renormalization group, and quantum Monte-Carlo.