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

TL;DR

This paper critically examines a recent study on quantum phase transitions in a specific model, revealing discrepancies in the reported transition point and suggesting alternative ground state configurations, thus challenging prior conclusions.

Contribution

It provides a critical analysis of previous results, highlighting inaccuracies in the phase transition point and proposing the instability of the assumed dimer state.

Findings

Kotov et al.'s transition point is inaccurate compared to QMC results.

The referenced dimer state is unstable against a plaquette condensate.

The actual transition point lies in an unexplored parameter region.

Abstract

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 previous quantum Monte-Carlo (QMC) results. In this Comment we show that the above claim is misleading and in reality their phase transition point is not only far from the corresponding QMC value but also lies in a region of parameter space not yet explored in the literature. We also show that their reference dimer state is unstable against formation of a plaquette condensate, which could in part explain the large fluctuations they found.