Edge and impurity response in two-dimensional quantum antiferromagnets

Abstract

Motivated by recent Monte-Carlo simulations of Hoglund and Sandvik (arXiv:0808.0408), we study edge response in square lattice quantum antiferromagnets. We use the O(3) non-linear sigma-model to compute the decay asymptotics of the staggered magnetization, energy density and local magnetic susceptibility away from the edge. We find that the total edge susceptibility is negative and diverges logarithmically as the temperature vanishes. We confirm the predictions of the continuum theory by performing a 1/S expansion of the microscopic Heisenberg model with the edge. We propose a qualitative explanation of the edge dimerization seen in Monte-Carlo simulations by a theory of valence-bond-solid correlations in the Neel state. We also discuss the extension of the latter theory to the response of a single non-magnetic impurity, and its connection to the theory of the deconfined critical point.

25 pages, 6 figures

References in corpus (12)

• "Deconfined" quantum critical points
• Quantum criticality beyond the Landau-Ginzburg-Wilson paradigm
• Evidence for deconfined quantum criticality in a two-dimensional Heisenberg model with four-spin interactions
• Finite-Size Scaling of the Ground State Parameters of the Two-Dimensional Heisenberg Model
• The Theory of Boundary Critical Phenomena
• Emergent Photons and New Transitions in the O(3) Sigma Model with Hedgehog Suppression
• Scaling in the Fan of an Unconventional Quantum Critical Point
• Universal Magnetic Properties of $L{a}_{2-\delta }S{r}_{\delta }Cu{O}_4$ at Intermediate Temperatures
• Theory of quantum impurities in spin liquids
• Valence bond solid order near impurities in two-dimensional quantum antiferromagnets
• Imaging bond order near non-magnetic impurities in square lattice antiferromagnets
• Impurity spin textures across conventional and deconfined quantum critical points of two-dimensional antiferromagnets

Cited by in corpus (10)

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• Heisenberg antiferromagnet on Cayley trees: low-energy spectrum and even/odd site imbalance
• Spin correlations near the edge as probe of Dimer order in square-lattice Heisenberg models
• Edge effects in the two-dimensional spin-1/2 Heisenberg antiferromagnet
• Effects of edge disorder in nano-scale antiferromagnetic clusters
• Spin correlations near the surface of a three-dimensional Heisenberg antiferromagnet
• Near-Boundary and Bulk Regions of a Semi-Infinite Two-Dimensional Heisenberg Antiferromagnet
• Many-body calculation of the spatial extent of the wave-function of a non-magnetic impurity in a d-wave high-temperature superconductor using the t--J model
• The t-J model on a semi-infinite lattice
• Excitations and spin correlations near the interface of two three-dimensional Heisenberg antiferromagnets