  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.
