Néel to dimer transition in spin-Santiferromagnets: 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, and 3/2. Using exact stochastic series expansion quantum Monte Carlo (QMC) calculations, we find that the critical value of the interlayer coupling, J ⊥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 ⊥c [S] ∝ S(S + 1), in qualitative accord with QMC, but the resulting J ⊥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 we show that including these within a perturbative scheme leads to reasonable agreement with QMC results for S = 1 and 3/2. We discuss the broad implications of our results for systems such as the triangular lattice S = 1 dimer compound Ba 3 Mn 2 O 8 and the S = 3/2 bilayer honeycomb material Bi 3 Mn 4 O 12 (NO 3 ).

Dynamical structure factors and excitation modes of the bilayer Heisenberg model

“…In this approach one introduces bosonic operators corresponding to spin-1 excitations (often called triplons 26 ) atop a singlet background 39,40 . Generalisations of the bond-operator approach to magnetically ordered states 22 and to arbitrary spin 41 have been investigated in the past. Moreover, it was recently shown 42,43 that bond operators enable a controlled description of coupled-dimer systems across the entire phase diagram using 1/d as a small parameter, where d is the spatial dimension: relevant observables can be obtained in a systematic 1/d expansion once the dimer lattice has been generalized to d space dimensions (for details we refer to Refs.…”

Frustrated spin- 12 Heisenberg magnet on a square-lattice bilayer: High-order study of the quantum critical behavior of the J1−J2−J

“…model on a square-lattice bilayer has been studied previously [86][87][88][89][90][91][92][93][94][95][96][97][98][99][100][101][102]. Since QMC calculations can be performed in this case (i.e., when κ = 0), the position δ > c 1 (κ = 0) of the QPT between the Néel-ordered state and the quantum disordered interlayer-dimer VBC (IDVBC) state can be ascertained with high accuracy.…”

High-order study of the quantum critical behavior of a frustrated spin- 12 antiferromagnet on a stacked honeycomb bilayer

“…The simplest such bilayer models comprise two layers stacked directly on top of one another and with only NN bonds, where the intralayer bonds all have equal strength J 1 and the interlayer (dimer) bonds all have equal strength J ⊥ 1 . Such models on the square lattice, where the bonds compete without frustration, have been studied fairly extensively [28][29][30][31][32]. As the ratio J ⊥ 1 /J 1 is increased beyond a critical value (J ⊥ 1 /J 1 ) c a QPT occurs from a Néel-ordered GS phase to a paramagnetic GS phase that is approximately the product of interlayer dimer valence bonds between NN pairs coupled by J ⊥ 1 bonds.…”

“…Since the AA stacking yields the simpler form of coupled-dimer magnets we restrict attention here to this form of honeycomb bilayer. After the unfrustrated J 1 -J ⊥ 1 honeycomb bilayer was studied [32], various authors have studied the effects of both intralayer frustration [38][39][40][41] and interlayer frustration [42][43][44] on the system, by including NNN interactions between spins within the layers or between the layers, respectively. In the latter case the model has been studied both in the absence [42] and presence [43,44] [45,46] form a frustrated spin-1 2 AA-stacked bilayer honeycomb lattice.…”

“…[37]) relevant to bilayer graphene and in the AA stacking (see, e.g., Refs. [32,[38][39][40][41][42][43][44]) where the two layers are stacked directly on top of one another. Since the AA stacking yields the simpler form of coupled-dimer magnets we restrict attention here to this form of honeycomb bilayer.…”