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

Abstract

We study the effect of a missing spin in a one-dimensional S=1/2 antiferromagnet with nearest-neighbor Heisenberg exchange J and six-spin coupling Q=4qJ using quantum Monte-Carlo (QMC) and bosonization techniques. For q<q_c≈0.04, the system is in a quasilong 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 Φ(r)=⟨G↑|S^z(r)|G↑⟩ in the the S^z_tot=1/2 ground state |G↑⟩ 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.