Spin-1/2 Heisenberg antiferromagnet on an anisotropic kagome lattice

Abstract

We use the coupled cluster method to study the zero-temperature properties of an extended two-dimensional Heisenberg antiferromagnet formed from spin-1/2 moments on an infinite spatially anisotropic kagome lattice of corner-sharing isosceles triangles, with nearest-neighbor bonds only. The bonds have exchange constants $J_{1}>0$ along two of the three lattice directions and $J_{2} \equiv κJ_{1} > 0$ along the third. In the classical limit the ground-state (GS) phase for $κ< 1/2$ has collinear ferrimagnetic (Néel$'$) order where the $J_2$-coupled chain spins are ferromagnetically ordered in one direction with the remaining spins aligned in the opposite direction, while for $κ> 1/2$ there exists an infinite GS family of canted ferrimagnetic spin states, which are energetically degenerate. For the spin-1/2 case we find that quantum analogs of both these classical states continue to exist as stable GS phases in some regions of the anisotropy parameter $κ$, namely for $0<κ<κ_{c_1}$ for the Néel$'$ state and for (at least part of) the region $κ>κ_{c_2}$ for the canted phase. However, they are now separated by a paramagnetic phase without either sort of magnetic order in the region $κ_{c_1} < κ< κ_{c_2}$, which includes the isotropic kagome point $κ= 1$ where the stable GS phase is now believed to be a topological ($\mathbb{Z}_2$) spin liquid. Our best numerical estimates are $κ_{c_1} = 0.515 \pm 0.015$ and $κ_{c_2} = 1.82 \pm 0.03$.