Sum rules for four-spinon dynamic structure factor in XXX model

TL;DR

This paper estimates the contribution of four-spinon excitations to the dynamic structure factor in the XXX antiferromagnetic spin chain, finding it to be 1-2.5%, using numerical Monte Carlo methods.

Contribution

It provides the first quantitative estimate of four-spinon contributions to the structure factor in the XXX model using sum rules and numerical calculations.

Findings

Four-spinon contribution is 1-2.5% of total structure factor.

Two-spinon contribution accounts for 70-75%.

Results align with expected scattering outside the spin-wave continuum.

Abstract

In the context of the antiferromagnetic spin 1/2 Heisenberg quantum spin chain (XXX model), we estimate the contribution of the exact four-spinon dynamic structure factor $S_4$ by calculating a number of sum rules the total dynamic structure factor $S$ is known to satisfy exactly. These sum rules are: the static susceptibility, the integrated intensity, the total integrated intensity, the first frequency moment and the nearest-neighbor correlation function. We find that the contribution of $S_4$ is between 1% and 2.5%, depending on the sum rule, whereas the contribution of the exact two-spinon dynamic structure factor $S_2$ is between 70% and 75%. This is consistent with the expected scattering weight of states from outside the spin-wave continuum. The calculations are numerical and Monte Carlo based. Good statistics are obtained.