The dynamic structure factor in impurity-doped spin chains in a magnetic field

We consider the dynamic structure factor in impurity doped spin-1/2 chains for general anisotropy, magnetic field and momentum. The impurities lead to effectively isolated finite chain segments with a discrete spectrum and characteristic correlations, which have a distinct effect on the dynamic structure factor. We present very accurate results for the low energy spectral weight obtained by numerical Density Matrix Renormalization Group techniques and identify the character of dominant excitations. We find that due to the impurities spectral weight is shifted away from the two-particle continuum into regions where no signal would be expected for undoped chains. Further, we compare with bosonization and find surprisingly good agreement with the numerical results. This has direct relevance for recent experiments on spin chains and ultracold gases and shows that, contrary to expectations, bosonization works especially well for short chains and in the vicinity of divergences.