Quantum paramagnetic ground states on the honeycomb lattice and field-induced transition to Néel 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 Néel order melts beyond a critical $J_2$. The critical $J_2$ increases with a magnetic field, implying the existence of a field-induced paramagnet-Néel 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 Néel-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 Néel 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.

8 pages, revised longer version of arXiv:1012.0316. Corrected factor of 2 error in Eq.[16], replotted Fig.[4] and revised the critical $J_c/J_1$ needed to stabilize interlayer dimer state. We thank S. V. Isakov for discussions which uncovered this error

References in corpus (7)

• Bose-Einstein Condensation in Magnetic Insulators
• Quantum spin-liquid emerging in two-dimensional correlated Dirac fermions
• Affleck-Kennedy-Lieb-Tasaki State on a Honeycomb Lattice is a Universal Quantum Computational Resource
• Disordered Ground State and Magnetic Field-Induced Long-Range Order in an S=3/2 Antiferromagnetic Honeycomb Lattice Compound Bi3Mn4O12(NO3)
• Spin-gap phase of a quantum spin system on a honeycomb lattice
• Bond-operators and triplon analysis for spin-S dimer antiferromagnets
• Variational RVB wave function for the spin-1/2 Heisenberg Model on honeycomb lattice

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