Valence bond solid order near impurities in two-dimensional quantum antiferromagnets
Max A. Metlitski and Subir Sachdev

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 {\em et al.}, Science {\bf 315}, 1380 (2007)). 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 N\'eel state to a spin-gap state with long-range VBS order. We identify two distinct classes of impurities: ({\em i\/}) local modulation in the exchange constants, and ({\em 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 vortex in the VBS order 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.

© 2008 The American Physical Society.