Paper detail

The ground-state phase diagram of the XXZ spin-s kagome antiferromagnet: A coupled-cluster study

We use the coupled cluster method to high orders of approximation in order to calculate the ground-state phase diagram of the XXZ spin-$s$ kagome antiferromagnet with easy-plane anisotropy, i.e. the anisotropy parameter $Δ$ varies between $Δ=1$ (isotropic Heisenberg model) and $Δ=0$ ($XY$ model). We find that for the extreme quantum case $s=1/2$ the ground state is magnetically disordered in the entire region $0 \le Δ\le 1$. For $s=1$ the ground state is disordered for $0.818 < Δ\le 1$, it exhibits $\sqrt{3}\times\sqrt{3}$ magnetic long-range order for $0.281 < Δ<0.818$, and $q=0$ magnetic long-range order for $0 \le Δ< 0.281$. We confirm the recent result of Chernyshev and Zhitomirsky (Phys. Rev. Lett. 113, 237202 (2014)) that the selection of the ground state by quantum fluctuations is different for small $Δ$ ($XY$ limit) and for $Δ$ close to one (Heisenberg limit), i.e., $q=0$ magnetic order is favored over $\sqrt{3}\times\sqrt{3}$ for $0\le Δ<Δ_c$ and vice versa for $Δ_c < Δ\le 1$. We calculate $Δ_c$ as a function of the spin quantum number $s$.