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

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