Evaluation of Dynamic spin structure factor for the spin-1/2 XXZ chain in a magnetic field

TL;DR

This paper numerically evaluates the zero-temperature dynamic spin structure factor of the spin-1/2 XXZ chain in a magnetic field, confirming theoretical predictions and revealing a small peak near the upper boundary.

Contribution

It provides a detailed numerical analysis of the dynamic spin structure factor using Bethe ansatz form factors, confirming critical exponents and discovering new spectral features.

Findings

Transition rates approach 1 as delta approaches 0.

Critical exponents match conformal field theory predictions.

A small peak appears near the upper boundary for 0<delta<1.

Abstract

Transition rates and dynamic spin structure factor at zero temperature for the spin-1/2 XXZ chain at critical regime in a magnetic field are numerically evaluated in terms of the exact determinant representations for the form factors and norms of the Bethe eigenstates. We have seen that the transition rates converges toward the constant function with the value 1 in the limit delta -> 0. The observed critical exponent of the singularity at the lower boundary is compared with the one predicted from the comformal field theory. We confirm that they are in good agreement. Further we have discovered that a small peak emerges near the upper boundary in the line shape of S(q,omega) for 0<delta<1.