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 $J_2\equiv \kappa J_1>0$ along the third. In the classical limit the ground-state (GS) phase for $\kappa <1/2$ has collinear ferrimagnetic (Néel${}^{\prime }$) 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 $\kappa >1/2$ 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 $\kappa$, namely for $0<\kappa <{\kappa }_{c_1}$ for the Néel${}^{\prime }$ state and for (at least part of) the region $\kappa >{\kappa }_{c_2}$ for the canted phase. However, they are now separated by a paramagnetic phase without either sort of magnetic order in the region ${\kappa }_{c_1}<\kappa <{\kappa }_{c_2}$, which includes the isotropic kagome point $\kappa =1$ where the stable GS phase is now believed to be a topological (${\mathbb{Z}}_2$) spin liquid. Our best numerical estimates are ${\kappa }_{c_1}=0.515\pm 0.015$ and ${\kappa }_{c_2}=1.82\pm 0.03$.

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