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

TL;DR

This paper investigates how missing spins affect the spin texture in a one-dimensional $S=1/2$ antiferromagnetic chain, revealing scaling behaviors and the influence of marginal interactions through QMC and bosonization.

Contribution

It combines Quantum Monte Carlo and bosonization techniques to analyze vacancy-induced spin textures and the role of marginally irrelevant interactions in a 1D antiferromagnetic system.

Findings

QMC results match bosonization predictions at critical coupling q_c

Scaling violations occur for q < q_c due to marginal interactions

Field theory accurately describes the spin texture behavior

Abstract

We study the effect of a missing spin in a one dimensional $S=1/2$ 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 $\Phi(r) = <G_{\uparrow}|S^z(r)|G_{\uparrow}>$ in the the $S^z_{tot}=1/2$ ground state $|G_{\uparrow}>$ of the system with a missing spin, focusing on the 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 $q < q_c$.