The dynamic structure factor in impurity-doped spin chains

TL;DR

This paper investigates how impurities in spin-1/2 Heisenberg chains alter the dynamic structure factor, providing detailed predictions using bosonization and DMRG, revealing spectral weight shifts caused by impurities.

Contribution

It offers a quantitative analysis of impurity effects on the structure factor in doped spin chains using combined analytical and numerical methods.

Findings

Spectral weight shifts away from $k=\pi$ due to impurities.

Scaling functions describe the spectral changes.

Finite segments exhibit discrete spectra and correlations.

Abstract

The effects of impurities in spin-1/2 Heisenberg chains are recently experiencing a renewed interest due to experimental realizations in solid state systems and ultra-cold gases. The impurities effectively cut the chains into finite segments with a discrete spectrum and characteristic correlations, which have a distinct effect on the dynamic structure factor. Using bosonization and the numerical Density Matrix Renormalization Group we provide detailed quantitative predictions for the momentum and energy resolved structure factor in doped systems. Due to the impurities, spectral weight is shifted away from the antiferromagnetic wave-vector $k=\pi$ into regions which normally have no spectral weight in the thermodynamic limit. The effect can be quantitatively described in terms of scaling functions, which are derived from a recurrence relation based on bosonization.