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

TL;DR

This paper investigates how magnetic fields induce transitions from quantum paramagnetic states to Ne9el order in honeycomb lattice spin models, combining theoretical and numerical methods to reveal critical points and phase changes.

Contribution

It introduces a comprehensive analysis of field-induced magnetic transitions in honeycomb lattice models, including frustrated, bilayer, and AKLT-like systems, using spin wave theory, bond operator mean field, and exact diagonalization.

Findings

Critical J_2 increases with magnetic field, enabling a paramagnet-Ne9el transition.

Field induces Ne9el order in bilayer models with interlayer dimer states.

AKLT state undergoes a field-induced transition to Ne9el order.

Abstract

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.