Quantum $J_1$--$J_2$ antiferromagnet on the stacked square lattice: Influence of the interlayer coupling on the ground-state magnetic ordering

Abstract

Using the coupled-cluster method (CCM) and the rotation-invariant Green's function method (RGM), we study the influence of the interlayer coupling $J_{\perp }$ on the magnetic ordering in the ground state of the spin-1/2 $J_1$-$J_2$ frustrated Heisenberg antiferromagnet ($J_1$-$J_2$ model) on the stacked square lattice. In agreement with known results for the $J_1$-$J_2$ model on the strictly two-dimensional square lattice ($J_{\perp }=0$) we find that the phases with magnetic long-range order at small $J_2<J_{c_1}$ and large $J_2>J_{c_2}$ are separated by a magnetically disordered (quantum paramagnetic) ground-state phase. Increasing the interlayer coupling $J_{\perp }>0$ the parameter region of this phase decreases, and, finally, the quantum paramagnetic phase disappears for quite small $J_{\perp }\sim \mathrm{0.2...0.3}{J}_1$.

arXiv comment4 pages, 3 figures

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