A frustrated spin-1/2 Heisenberg antiferromagnet on a chevron-square lattice

Abstract

The coupled cluster method (CCM) is used to study the zero-temperature properties of a frustrated spin-half ($s=12$) $J_1$--$J_2$ Heisenberg antiferromagnet (HAF) on a 2D chevron-square lattice. Each site on an underlying square lattice has 4 nearest-neighbor exchange bonds of strength $J_1>0$ and 2 next-nearest-neighbor (diagonal) bonds of strength $J_2\equiv x{J}_1>0$, with each square plaquette having only one diagonal bond. The diagonal bonds form a chevron pattern, and the model thus interpolates smoothly between 2D HAFs on the square ($x=0$) and triangular ($x=1$) lattices, and also extrapolates to disconnected 1D HAF chains ($x\to \infty$). The classical ($s\to \infty$) version of the model has Néel order for $0<x<x_{\mathrm{cl}}$ and a form of spiral order for $x_{\mathrm{cl}}<x<\infty$, where $x_{\mathrm{cl}}=12$. 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 scheme, which we carry out to high orders and extrapolate to the physical limit. 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 that the $s=12$ model has two quantum critical points, at $x_{c_1}\approx 0.72(1)$ and $x_{c_2}\approx 1.5(1)$, with Néel order for $0<x<x_{c_1}$, a form of spiral order for $x_{c_1}<x<x_{c_2}$ that includes the correct three-sublattice $120^{\circ }$ spin ordering for the triangular-lattice HAF at $x=1$, and parallel-dimer VBC order for $x_{c_2}<x<\infty$.

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• The frustrated spin-$\frac{1}{2}$ $J_1$--$J_2$ isotropic $XY$ model on the honeycomb lattice
• Interpolation between low and high temperatures of the specific heat for spin systems
• Ground-state phases of the spin-1 $J_1$--$J_2$ Heisenberg antiferromagnet on the honeycomb lattice
• Analytical and numerical studies of the one-dimensional sawtooth chain
• Spin-1/2 $J_1$-$J_2$ Heisenberg model on a cross-striped square lattice
• Frustration induced noncollinear magnetic order phase in one-dimensional Heisenberg chain with alternating antiferromagnetic and ferromagnetic next nearest neighbor interactions
• Ground-state phase structure of the spin-$\frac{1}{2}$ anisotropic planar pyrochlore
• A frustrated spin-1 $J_1$--$J_2$ Heisenberg antiferromagnet: An anisotropic planar pyrochlore model