Monte Carlo Study of Four-Spinon Dynamic Structure Function in Antiferromagnetic Heisenberg Model

TL;DR

This paper uses Monte Carlo methods to analyze the four-spinon dynamic structure function in the antiferromagnetic Heisenberg model, revealing its behavior, continuum region, and comparison with two-spinon functions.

Contribution

It provides a detailed Monte Carlo analysis of the four-spinon structure function and its continuum in the Heisenberg model, a novel computational approach for this problem.

Findings

Behavior of $S_4$ aligns with the four-spinon continuum

$S_4$ is zero outside the continuum region

Shape of $S_4$ similar to $S_2$

Abstract

Using Monte Carlo integration methods, we describe the behavior of the exact four-spinon dynamic structure function $S_{4}$ in the antiferromagnetic spin 1/2 Heisenberg quantum spin chain as a function of the neutron energy $\omega$ and momentum transfer $k$. We also determine the four-spinon continuum, the extent of the region in the $(k,\omega)$ plane outside which $S_{4}$ is identically zero. In each case, the behavior of $S_{4}$ is shown to be consistent with the four-spinon continuum and compared to the one of the exact two-spinon dynamic structure function $S_{2}$. Overall shape similarity is noted.