Phase diagram of a frustrated Heisenberg antiferromagnet on the honeycomb lattice: The J 1-J 2-J 3 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 J 1-J 2-J 3 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 J 1 1, we find four magnetically ordered phases in the parameter window J 2,J 3[0,1], namely, the Néel, striped, and Néel-II collinear AFM phases, plus a spiral phase. The Néel-II phase appears as a stable GS phase in the classical version of the model only for values J 3<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) (J2c 1,J3c 1)=(0.51±0.01,0.69±0.01) between the Néel, striped, and QP phases; (b) (J2c 2,J3c 2)=(0.65±0.02,0.55±0.01) between the striped, spiral, and QP phases; and (c) (J2c 3,J3c 3)=(0.69±0.01,0. 12±0.01) between the spiral, Néel-II, and QP phases.

Original languageEnglish (US)
Article number144404
JournalPhysical Review B - Condensed Matter and Materials Physics
Issue number14
StatePublished - Oct 9 2012

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