Finite Size Analysis of the Structure Factors in the Antiferromagnetic XXZ Model

TL;DR

This paper analyzes the finite size effects on structure factors in the antiferromagnetic XXZ model, comparing numerical results with exact solutions and previous conjectures to identify agreements and discrepancies.

Contribution

It provides a detailed finite size analysis of structure factors in the XXZ model and compares these with exact and conjectured results, highlighting where they agree or differ.

Findings

Excellent agreement with Tonegawa's exact results for the XX model

Discrepancies found in the momentum dependence of the longitudinal structure factors compared to previous conjectures

Provides insights into finite size effects in the antiferromagnetic XXZ model

Abstract

We perform a finite size analysis of the longitudinal and transverse structure factors $S_j(p,\gamma,N),j=1,3$ in the groundstate of the spin-$\frac{1}{2}$ XXZ model. Comparison with the exact results of Tonegawa for the XX model yields excellent agreement. Comparison with the conjecture of M\"uller, Thomas, Puga and Beck reveals discrepancies in the momentum dependence of the longitudinal structure factors.