Plaquette valence-bond solid in the square-latticeJ1-J2antiferromagnet Heisenberg model: A bond operator approach

Abstract

We study the plaquette valence-bond solid phase of the spin-1/2 J1-J2 antiferromagnet Heisenberg model on the square lattice within the bond-operator theory. We start by considering four S = 1/2 spins on a single plaquette and determine the bond operator representation for the spin operators in terms of singlet, triplet, and quintet boson operators. The formalism is then applied to the J1-J2 model and an effective interacting boson model in terms of singlets and triplets is derived. The effective model is analyzed within the harmonic approximation and the previous results of Zhitomirsky and Ueda [Phys. Rev. B 54, 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 the parameter region 0.34 < J2/J1 < 0.59, which is narrower than the harmonic one. Differently from the harmonic approximation, the excitation gap vanishes at both critical couplings J2 = 0.34 J1 and J2 = 0.59 J1. Interestingly, for J2 < 0.48 J1, the excitation gap corresponds to a singlet-triplet excitation at the Γ point while, for J2 > 0.48 J1, it is related to a singlet-singlet excitation at the X = (π/2, 0) point of the tetramerized Brillouin zone.

Phase diagram of J1-J2 transverse field Ising model on the checkerboard lattice: a plaquette-operator approach

“…The RVB scenario has received a great impact to elucidate the plaquette RVB phase in the s=1/2 honeycomb J 1 − J 2 Heisenberg model 8,9 , which is justified by the two-dimensional approach of density matrix renormalization group, recently 10,11 . It gives the impression that the plaquette type ordered phase is a result of strong correlation and frustration, which has also been observed in the square lattice [12][13][14][15][16] . According to Ref.…”

“…According to Ref. 15 , which shows that a plaquette phase is stable in the range of parameters, where a spin-liquid phase has been reported 16,17 , it is interesting to investigae the spin-liquid phase within a plaquette operator approach.…”

Low-energy singlet sector in the spin-1/2 J 1–J 2 Heisenberg model on a square lattice

“…Despite a great deal of interest which this model has attracted during the last quarter of a century, its properties remain a puzzle in the most frustrated regime of 0.4 J 2 0.6. This problem has been attacked using many powerful numerical and analytical methods including variational MonteCarlo (VMC) calculations, 1,2 density matrix renormalization group (DMRG) method, 3,4 coupled cluster method (CCM), 5,6 plaquette 7,8 and dimer 9-11 series expansions, tensor network state approach, 12,13 exact diagonalization, [14][15][16] spin-wave analysis, 17 large-N expansion, 18,19 hierarchical mean-field approach, 20 bond operator approach, [21][22][23] functional renormalization group, 24 and some others. It is generally believed that Néel ordered phases with AF vectors (π, π) and (0, π) (or (π, 0)) arise at J 2 0.4 and J 2 0.6, respectively.…”

Block product density matrix embedding theory for strongly correlated spin systems

“…The nature of the intermediate paramagnetic phase is still undecided. Multiple interpretations for this phase have been proposed, such as spin liquids and valence bond states like the columnar and staggered dimer valence bond crystals and the plaquette resonating valence bond (PRVB) state [12,[19][20][21][55][56][57][58][59][60][61][62][63][64]. In Ref.…”