Two-spinon dynamic structure factor of the one-dimensional S=1/2 Heisenberg antiferromagnet

TL;DR

This paper evaluates the exact 2-spinon contribution to the dynamic structure factor of the 1D S=1/2 Heisenberg antiferromagnet at zero temperature, comparing it with finite-chain data and analyzing its spectral properties.

Contribution

It provides a detailed evaluation of the exact 2-spinon dynamic structure factor and its singularity structure, enhancing understanding of spin excitations in the model.

Findings

2-spinon excitations account for 72.89% of total intensity

Singularity structure of the exact result is analytically determined

Spectral-weight distribution is numerically evaluated across the continuum

Abstract

The exact expression derived by Bougourzi, Couture, and Kacir for the 2-spinon contribution to the dynamic spin structure factor $S_{zz}(q,\omega)$ of he one-dimensional $S$=1/2 Heisenberg antiferromagnet at $T=0$ is evaluated for direct comparison with finite-chain transition rates ($N\leq 28$) and an approximate analytical result previously inferred from finite-$N$ data, sum rules, and Bethe-ansatz calculations. The 2-spinon excitations account for 72.89% of the total intensity in $S_{zz}(q,\omega)$. The singularity structure of the exact result is determined analytically and its spectral-weight distribution evaluated numerically over the entire range of the 2-spinon continuum. The leading singularities of the frequency-dependent spin autocorrelation function, static spin structure factor, and $q$-dependent susceptibility are determined via sum rules.