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In a recent paper [Phys. Rev. {\bf B80}, 174403 (2009)] Kotov {\it et al.}studied the paramagnetic-to-antiferromagnetic transition in the $J$-$Q$ model.Their findings were claimed to be in "fairly good agreement" with previousquantum Monte-Carlo (QMC) results. In this Comment we show that the above claimis misleading and in reality their phase transition point is not only far fromthe corresponding QMC value but also lies in a region of parameter space notyet explored in the literature. We also show that their reference dimer stateis unstable against formation of a plaquette condensate, which could in partexplain the large fluctuations they found.

Comment on "Quantum phase transition in the four-spin exchange antiferromagnet" by V. N. Kotov, D.-X. Yao, A. H. Castro-Neto, and D. K. Campbell