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.
Highlights
A number of recent scanning tunnelling microscopy experiments have highlighted spatial modulations in the local density of states in the cuprate compounds, nucleated by external perturbations
In Ref. 5, similar charge-ordering patterns were found to be ubiquitous in the underdoped cuprates at low temperatures, and it was established that the charge ordering was “bond-centered”, and had an anisotropic structure similar to a valence bond solid state[6,7,8,9]
This paper began with the theory S in Eq (1.1) for square lattice quantum antiferromagnets in the vicinity of a Neel-valence bond solid (VBS) quantum phase transitions
Summary
A number of recent scanning tunnelling microscopy experiments have highlighted spatial modulations in the local density of states in the cuprate compounds, nucleated by external perturbations. In the light of these observations, it is of general interest to study the appearance of varieties of charge order (including “valence bond solid” (VBS) order8–10) near impurities in strongly correlated systems For superfluid states, such a theory has been presented in earlier work[11,12], and compared quantitatively with some of the above experiments. The primary focus of the present paper is on a distinct class of impurities, in which the valence-bond structure of the non-magnetic ground state of the antiferromagnet is more strongly disrupted, and a “Berry phase” contribution of an unpaired spin is the crucial impurity-induced perturbation[18,19]. The following subsections will describe the two classes of impurity perturbations to the theory S shown in Figs. 1 and 2 respectively
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