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

TL;DR

This study compares bond operator theory and quantum Monte Carlo simulations to analyze the Nél to dimer transition in spin-S bilayer antiferromagnets, revealing the importance of high-energy modes for accurate predictions.

Contribution

The paper provides a detailed comparison between bond operator mean field theory and QMC simulations for various spin values, highlighting the significance of high-energy modes in modeling the transition.

Findings

Critical interlayer coupling increases with spin S.

Transition belongs to the O(3) universality class for all S.

Including high-energy quintet modes improves theoretical predictions.

Abstract

We study the N\'eel 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}).