Edge and impurity response in two-dimensional quantum antiferromagnets

TL;DR

This paper investigates the edge and impurity responses in two-dimensional quantum antiferromagnets using continuum field theory and microscopic models, revealing divergence in edge susceptibility and explaining edge dimerization phenomena.

Contribution

It provides a theoretical analysis of edge and impurity effects in quantum antiferromagnets, confirming continuum predictions with microscopic calculations and proposing a valence-bond-solid correlation explanation.

Findings

Edge susceptibility diverges logarithmically at low temperatures.

Continuum theory predictions are confirmed by 1/S expansion of the Heisenberg model.

Edge dimerization is explained via valence-bond-solid correlations.

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.