Valence bond solid order near impurities in two-dimensional quantum antiferromagnets

TL;DR

This paper develops a theory describing how valence bond solid order is affected near impurities in two-dimensional quantum antiferromagnets, with implications for understanding STM experiments in cuprates.

Contribution

It introduces a boundary critical theory for VBS order near impurities, distinguishing two impurity classes and predicting a VBS pinwheel structure.

Findings

Identification of two impurity classes affecting VBS order.

Prediction of a VBS pinwheel structure around certain impurities.

Suppression of VBS susceptibility near impurities.

Abstract

Recent scanning tunnelling microscopy (STM) experiments on underdoped cuprates have displayed modulations in the local electronic density of states which are centered on a Cu-O-Cu bond (Kohsaka et. al., cond-mat/0703309). As a paradigm of the pinning of such bond-centered ordering in strongly correlated systems, we present the theory of valence bond solid (VBS) correlations near a single impurity in a square lattice antiferromagnet. The antiferromagnet is assumed to be in the vicinity of a quantum transition from a magnetically ordered Neel state to a spin-gap state with long-range VBS order. We identify two distinct classes of impurities: i) local modulation in the exchange constants, and ii) a missing or additional spin, for which the impurity perturbation is represented by an uncompensated Berry phase. The `boundary' critical theory for these classes is developed: in the second class we find a `VBS pinwheel' around the impurity, accompanied by a suppression in the VBS susceptibility. Implications for numerical studies of quantum antiferromagnets and for STM experiments on the cuprates are noted.