Vacancy-induced spin texture in a one dimensional $S=1\mathrm{/}2$ Heisenberg antiferromagnet

We study the effect of a missing spin in a one dimensional $S=1\mathrm{/}2$ antiferromagnet with nearest neighbour Heisenberg exchange $J$ and six-spin coupling $Q=4qJ$ using Quantum Monte-Carlo (QMC) and bosonization techniques. For $q<q_c\approx 0.04$, the system is in a quasi-long range ordered power-law antiferromagnetic phase, which gives way to a valence-bond solid state that spontaneously breaks lattice translation symmetry for $q>q_c$. We study the ground state spin texture $\Phi® = <G_{\uparrow}|S^z®|G_{\uparrow}>$inthethe$S^z_{tot}=1/2$groundstate$|G_{\uparrow}>$ of the system with a missing spin, focusing on the alternating part $N_z(r)$. We find that our QMC results for $N_z$ at $q=q_c$ take on the scaling form expected from bosonization considerations, but violate scaling for $q<q_c$. Within the bosonization approach, such violations of scaling arise from the presence of a marginally irrelevant sine-Gordon interaction, whose effects we calculate using renormalization group (RG) improved perturbation theory. Our field-theoretical predictions are found to agree well with the QMC data for $q<q_c$.