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 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 $S_{tot}^z=1/2$ 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 $q<q_c$.

9 pages, two-column PRB format

References in corpus (12)

• Quantum criticality beyond the Landau-Ginzburg-Wilson paradigm
• Evidence for deconfined quantum criticality in a two-dimensional Heisenberg model with four-spin interactions
• Antiferromagnetic to valence-bond-soild transitions in two-dimensional SU(N) Heisenberg models with multi-spin interactions
• Continuous quantum phase transition between an antiferromagnet and a valence-bond-solid in two dimensions; evidence for logarithmic corrections to scaling
• Loop updates for variational and projector quantum Monte Carlo simulations in the valence-bond basis
• Impurity spin texture at a deconfined quantum critical point
• Quantum criticality in SU(3) and SU(4) anti-ferromagnets
• Thermodynamics of a gas of deconfined bosonic spinons in two dimensions
• Impurity spin texture at a Néel-Valence Bond Solid critical point in $d=2$ SU(3) quantum antiferromagnets
• Quantitative expression of the spin gap via bosonization for a dimerized spin-1/2 chain
• Generalization of the singlet sector valence bond loop algorithm to antiferromagnetic ground states with total spin $S_{tot}=1/2$
• NMR Response in quasi one-dimensional Spin-1/2 Antiferromagnets

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• Deconfined quantum criticality in spin-1/2 chains with long-range interactions
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• Numerical Investigations of SO(4) Emergent Extended Symmetry in Spin-1/2 Heisenberg Antiferromagnetic Chains
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• Detecting emergent continuous symmetries at quantum criticality
• The Néel-VBS transition in three-dimensional SU($N$) antiferromagnets
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• Competition between Neel, Haldane nematic, plaquette valence bond solid, and $(\pi ,\pi )$ valence bond solid phases in SU(N) analogs of $S=1$ square-lattice antiferromagnets