Phase diagram of a frustrated Heisenberg antiferromagnet on the honeycomb lattice: The J1-J2-J3 model

P. H Y Li, R. F. Bishop, D. J J Farnell, C. E. Campbell

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    We use the coupled-cluster method in high orders of approximation to make a comprehensive study of the ground-state (GS) phase diagram of the spin-1/2 J1-J2-J3 model on a two-dimensional honeycomb lattice with antiferromagnetic (AFM) interactions up to third-nearest neighbors. Results are presented for the GS energy and the average local onsite magnetization. With the nearest-neighbor coupling strength J1 ≡ 1, we find four magnetically ordered phases in the parameter window J2,J3 ∈ [0,1], namely, the N´eel, striped, and N´eel-II collinear AFM phases, plus a spiral phase. The N´eel-II phase appears as a stable GS phase in the classical version of the model only for values J3 < 0. Each of these four ordered phases shares a boundary with a disordered quantum paramagnetic (QP) phase, and at several widely separated points on the phase boundaries the QP phase has an infinite susceptibility to plaquette valence-bond crystalline order. We identify all of the phase boundaries with good precision in the parameter window studied, and we find three tricritical quantum critical points therein at (a) (J2c1 , J3c1 ) = (0.51 ± 0.01,0.69 ± 0.01) between the N´eel, striped, and QP phases; (b) (J2c2 , J3c2) = (0.65 ± 0.02,0.55 ± 0.01) between the striped, spiral, and QP phases; and (c) (J2c3 , J3c3) = (0.69 ± 0.01,0.12 ± 0.01) between the spiral, N´eel-II, and QP phases.
    Original languageEnglish
    Article number144404 (12pp)
    JournalPhysical Review B (Condensed Matter and Materials Physics)
    Publication statusPublished - 2012


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