Frustrated spin-12 Heisenberg antiferromagnet on a chevron-square lattice

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

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The coupled cluster method (CCM) is used to study the zero-temperature properties of a frustrated spin-half (s=12) J1-J2 Heisenberg antiferromagnet (HAF) on a two-dimensional (2D) chevron-square lattice. On an underlying square lattice, each site of the model has four nearest-neighbor exchange bonds of strength J1>0 and two frustrating next-nearest-neighbor (diagonal) bonds of strength J 2≡κJ1>0, such that each fundamental square plaquette has only one diagonal bond. The diagonal J2 bonds are arranged in a chevron pattern such that along one of the two basic square axis directions (say, along rows), the J2 bonds are parallel, while along the perpendicular axis direction (say, along columns), alternate J2 bonds are perpendicular to each other, and hence form one-dimensional (1D) chevron chains in this direction. The model thus interpolates smoothly between 2D HAFs on the square (κ=0) and triangular (κ=1) lattices, and also extrapolates to disconnected 1D HAF chains (κ→∞). The classical (s→∞) version of the model has collinear Néel order for 0<κ<κcl and a form of noncollinear spiral order for κcl<κ<∞, where κcl=12. For the s=12 model, we use both these classical states, as well as other collinear states not realized as classical ground-state (GS) phases, as CCM reference states, on top of which the multispin-flip configurations resulting from quantum fluctuations are incorporated in a systematic truncation hierarchy, which we carry out to high orders and then extrapolate to the physical limit. At each order we calculate the GS energy, GS magnetic order parameter, and the susceptibilities of the states to various forms of valence-bond crystalline (VBC) order, including plaquette and two different dimer forms. We find strong evidence that the s=12 model has two quantum critical points, at κc1≈0.72(1) and κc2≈1.5(1), such that the system has Néel order for 0<κ<κc1, a form of spiral order for κc1<κ<κc2 that includes the correct three-sublattice 120â̂̃ spin ordering for the triangular-lattice HAF at κ=1, and parallel-dimer VBC order for κc2<κ<∞.

Original languageEnglish (US)
Article number144423
JournalPhysical Review B - Condensed Matter and Materials Physics
Issue number14
StatePublished - Oct 25 2013


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