Magnetization profiles and NMR spectra of doped Haldane chains at finite temperatures

Open segments of $S=1\mathrm{}$ antiferromagnetic spin chains are studied at finite temperatures and fields using continuous time quantum Monte Carlo techniques. By calculating the resulting magnetization profiles for a large range of chain lengths with fixed field and temperature we reconstruct the experimentally measured NMR spectrum of impurity doped ${\mathrm{Y}}_2{\mathrm{BaNi}}_{1-x}{\mathrm{Mg}}_x{\mathrm{O}}_5.$ For temperatures above the gap the calculated NMR spectra are in excellent agreement with the experimental results, confirming the existence of $S=1/2\mathrm{}$ excitations at the end of open $S=1\mathrm{}$ chain segments. At temperatures below the gap, neglecting interchain couplings, we still find well defined peaks in the calculated NMR spectra corresponding to the $S=1/2\mathrm{}$ chain end excitations. At low temperatures, interchain couplings could become important, resulting in a more complicated phase.