The dynamical spin structure factor for the anisotropic spin-1/2 Heisenberg chain

TL;DR

This paper investigates the dynamical spin structure factor of the anisotropic spin-1/2 Heisenberg chain using Bethe Ansatz, field theory, and DMRG, revealing non-Lorentzian peaks and the influence of integrability on lineshape.

Contribution

It provides a detailed analysis of the spin structure factor at small wave-vectors, including an analytic formula for the high-frequency tail and the impact of magnetic field and integrability.

Findings

Peak width scales as q^2 at finite magnetic field

High-frequency tail described by an analytic formula

Integrability influences the lineshape of the structure factor

Abstract

The longitudinal spin structure factor for the XXZ-chain at small wave-vector q is obtained using Bethe Ansatz, field theory methods and the Density Matrix Renormalization Group. It consists of a peak with peculiar, non-Lorentzian shape and a high-frequency tail. We show that the width of the peak is proportional to q^2 for finite magnetic field compared to q^3 for zero field. For the tail we derive an analytic formula without any adjustable parameters and demonstrate that the integrability of the model directly affects the lineshape.