Néel to dimer transition in spin-S antiferromagnets: Comparing bond operator theory with quantum Monte Carlo simulations for bilayer Heisenberg models

Abstract

We study the Néel to dimer transition driven by interlayer exchange coupling in spin-S Heisenberg antiferromagnets on bilayer square and honeycomb lattices for S=1/2, 1, 3/2. Using exact stochastic series expansion quantum Monte Carlo (QMC) calculations, we find that the critical value of the interlayer coupling, J_{\perp c}[S], increases with increasing S, with clear evidence that the transition is in the O(3) universality class for all S. Using bond operator mean field theory restricted to singlet and triplet states, we find J_{\perp c}[S] ~ S(S+1), in qualitative accord with QMC, but the resulting J_{\perp c} [S] is significantly smaller than the QMC value. For S=1/2, incorporating triplet-triplet interactions within a variational approach yields a critical interlayer coupling which agrees well with QMC. For higher spin, we argue that it is crucial to account for the high energy quintet modes, and show that including these within a perturbative scheme leads to reasonable agreement with QMC results for S=1,3/2. We discuss the broad implications of our results for systems such as the triangular lattice S=1 dimer compound Ba_3Mn_2O_8 and the S=3/2 bilayer honeycomb material Bi_3Mn_4O_{12}(NO_{3}).

14 pages, 7 figures, 2 tables. Updated data, corrected typos, added two paragraphs

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Cited by in corpus (22)

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• Non-linear bond-operator theory and 1/d expansion for coupled-dimer magnets I: Paramagnetic phase
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• Frustrated honeycomb-lattice bilayer quantum antiferromagnet in a magnetic field: Unconventional phase transitions in a two-dimensional isotropic Heisenberg model
• Origin of magnetic frustration in Bi${}_3$Mn${}_4$O${}_{12}$(NO${}_3$)
• A high-order study of the quantum critical behavior of a frustrated spin-$\frac{1}{2}$ antiferromagnet on a stacked honeycomb bilayer
• Frustrated magnetic interactions in an S=3/2 bilayer honeycomb lattice compound Bi3Mn4O12(NO3)
• Self consistent study of the quantum phases in a frustrated antiferromagnet on the bilayer honeycomb lattice
• Edge Magnon Excitation in Spin Dimer Systems
• Nematic quantum phases in the bilayer honeycomb antiferromagnet
• An effective field theory approach for the $S=3/2$ bilayer honeycomb antiferromagnet
• Extracting Universal Corner Entanglement Entropy during the Quantum Monte Carlo Simulation
• Collinear antiferromagnetic phases of a frustrated spin-$\frac{1}{2}$ $J_1$--$J_2$--$J_1^{\perp }$ Heisenberg model on an $AA$-stacked bilayer honeycomb lattice
• Transverse Magnetic Susceptibility of a Frustrated Spin-$\frac{1}{2}$ $J_1$--$J_2$--$J_1^{\perp }$ Heisenberg Antiferromagnet on a Bilayer Honeycomb Lattice
• Twisted superfluid and supersolid phases of triplons in bilayer honeycomb magnets
• Quantum to classical transition in the ground state of a spin-$S$ quantum antiferromagnet