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We study the plaquette valence-bond solid phase of the spin-1/2 J_1-J_2antiferromagnet Heisenberg model on the square lattice within the bond-operatortheory. We start by considering four S = 1/2 spins on a single plaquette anddetermine the bond operator representation for the spin operators in terms ofsinglet, triplet, and quintet boson operators. The formalism is then applied tothe J_1-J_2 model and an effective interacting boson model in terms of singletsand triplets is derived. The effective model is analyzed within the harmonicapproximation and the previous results of Zhitomirsky and Ueda [Phys. Rev. B54, 9007 (1996)] are recovered. By perturbatively including cubic(triplet-triplet-triplet and singlet-triplet-triplet) and quartic interactions,we find that the plaquette valence-bond solid phase is stable within theparameter region 0.34 < J_2/J_1 < 0.59, which is narrower than the harmonicone. Differently from the harmonic approximation, the excitation gap vanishesat both critical couplings J_2 = 0.34 J_1 and J_2 = 0.59 J_1. Interestingly,for J_2 < 0.48 J_1, the excitation gap corresponds to a singlet-tripletexcitation at the $\Gamma$ point while, for J_2 > 0.48 J_1, it is related to asinglet-singlet excitation at the X = (pi/2,0) point of the tetramerizedBrillouin zone.

Plaquette valence-bond solid in the square lattice J1-J2 antiferromagnet Heisenberg model: a bond operator approach