A high-order study of the quantum critical behavior of a frustrated spin-$\frac{1}{2}$ antiferromagnet on a stacked honeycomb bilayer

Abstract

We study a frustrated spin-$\frac{1}{2}$ $J_1$--$J_2$--$J_3$--$J_1^{\perp }$ Heisenberg antiferromagnet on an $AA$-stacked bilayer honeycomb lattice. In each layer we consider nearest-neighbor (NN), next-nearest-neighbor, and next-next-nearest-neighbor antiferromagnetic (AFM) exchange couplings $J_1$, $J_2$, and $J_3$, respectively. The two layers are coupled with an AFM NN exchange coupling $J_1^{\perp }\equiv \delta J_1$. The model is studied for arbitrary values of $\delta$ along the line $J_3=J_2\equiv \alpha J_1$ that includes the most highly frustrated point at $\alpha =\frac{1}{2}$, where the classical ground state is macroscopically degenerate. The coupled cluster method is used at high orders of approximation to calculate the magnetic order parameter and the triplet spin gap. We are thereby able to give an accurate description of the quantum phase diagram of the model in the $\alpha \delta$ plane in the window $0\le \alpha \le 1$, $0\le \delta \le 1$. This includes two AFM phases with Néel and striped order, and an intermediate gapped paramagnetic phase that exhibits various forms of valence-bond crystalline order. We obtain accurate estimations of the two phase boundaries, $\delta ={\delta }_{c_i}(\alpha )$, or equivalently, $\alpha ={\alpha }_{c_i}(\delta )$, with $i=1$ (Néel) and 2 (striped). The two boundaries exhibit an "avoided crossing" behavior with both curves being reentrant.

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Cited by in corpus (1)

• Frustrated spin-$\frac{1}{2}$ Heisenberg magnet on an $AA$-stacked honeycomb bilayer: High-order study of the collinear magnetic phases of the $J_1$--$J_2$--$J_1^{\perp }$ model