Spin-1/2 $J_1$-$J_2$ Heisenberg model on a cross-striped square lattice

Abstract

Using the coupled cluster method (CCM) we study the full (zero-temperature) ground-state (GS) phase diagram of a spin-half ($s=1/2$) $J_1$-$J_2$ Heisenberg model on a cross-striped square lattice. Each site of the square lattice has 4 nearest-neighbour exchange bonds of strength $J_1$ and 2 next-nearest-neighbour (diagonal) bonds of strength $J_2$. The $J_2$ bonds are arranged so that the basic square plaquettes in alternating columns have either both or no $J_2$ bonds included. The classical ($s\to \infty$) version of the model has 4 collinear phases when $J_1$ and $J_2$ can take either sign. Three phases are antiferromagnetic (AFM), showing so-called Néel, double Néel and double columnar striped order respectively, while the fourth is ferromagnetic. For the quantum $s=1/2$ model we use the 3 classical AFM phases as CCM reference states, on top of which the multispin-flip configurations arising from quantum fluctuations are incorporated in a systematic truncation hierarchy. Calculations of the corresponding GS energy, magnetic order parameter and the susceptibilities of the states to various forms of valence-bond crystalline (VBC) order are thus carried out numerically to high orders of approximation and then extrapolated to the (exact) physical limit. We find that the $s=1/2$ model has 5 phases, which correspond to the four classical phases plus a new quantum phase with plaquette VBC order. The positions of the 5 quantum critical points are determined with high accuracy. While all 4 phase transitions in the classical model are first order, we find strong evidence that 3 of the 5 quantum phase transitions in the $s=1/2$ model are of continuous deconfined type.

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• 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
• 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
• Coupled Cluster Treatment of the Alternating Bond Diamond Chain
• Gapped paramagnetic state in a frustrated spin-$\frac{1}{2}$ Heisenberg antiferromagnet on the cross-striped square lattice