Edge and Impurity Response in Two-Dimensional Quantum Antiferromagnets

Abstract

Motivated by recent Monte Carlo simulations of Höglund and Sandvik (arXiv:0808.0408), we study edge response in square lattice quantum antiferromagnets. We use the \(O(3)\) nonlinear σ 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 \(T\rightarrow 0\). 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 Néel state. We also discuss the extension of the latter theory to the response of a single nonmagnetic impurity, and its connection to the theory of the deconfined critical point.