Quantum paramagnetic ground states on the honeycomb lattice and field-induced transition to N\'eel order

Motivated by recent experiments on Bi$_3$Mn$_4$O$_{12}$(NO$_3$), and a broader interest arising from numerical work on the honeycomb lattice Hubbard model, we have studied the effect of a magnetic field on honeycomb lattice spin models with quantum paramagnetic ground states. For a model with frustrating second-neighbor exchange, $J_2$, we use a Lindemann-like criterion within spin wave theory to show that N\'eel order melts beyond a critical $J_2$. The critical $J_2$ increases with a magnetic field, implying the existence of a field-induced paramagnet-N\'eel transition over a range of $J_2$. We also study bilayer model using a spin-$S$ generalization of bond operator mean field theory. We show that there is a N\'eel-dimer transition for various spin values with increasing bilayer coupling, and that the resulting interlayer dimer state undergoes a field induced transition into a state with transverse N\'eel order. Finally, we study a spin-3/2 model which interpolates between the Heisenberg model and the Affleck-Kennedy-Lieb-Tasaki (AKLT) parent Hamiltonian. Using exact diagonalization, we compute the fidelity susceptibility to locate the Neel-AKLT quantum critical point, obtain the spin gap of the AKLT parent Hamiltonian, and argue that AKLT state also undergoes field-induced Neel ordering.