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

TL;DR

This study uses the coupled cluster method to map the ground-state phases of the XXZ kagome antiferromagnet across different spins and anisotropies, revealing quantum disordered and various ordered phases.

Contribution

It provides a detailed phase diagram for the XXZ kagome antiferromagnet for different spin values using high-order coupled cluster calculations, highlighting quantum fluctuation effects.

Findings

Quantum disordered ground state for s=1/2 across all anisotropies.

Identification of phase boundaries and magnetic order types for s=1.

Confirmation of quantum fluctuation-driven ground state selection near isotropic limit.

Abstract

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 $\Delta$ varies between $\Delta=1$ (isotropic Heisenberg model) and $\Delta=0$ ($XY$ model). We find that for the extreme quantum case $s=1/2$ the ground state is magnetically disordered in the entire region $0 \le \Delta \le 1$. For $s=1$ the ground state is disordered for $0.818 < \Delta \le 1$, it exhibits $\sqrt{3}\times\sqrt{3}$ magnetic long-range order for $0.281 < \Delta <0.818$, and $q=0$ magnetic long-range order for $0 \le \Delta < 0.281$. 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 $\Delta$ ($XY$ limit) and for $\Delta$ close to one (Heisenberg limit), i.e., $q=0$ magnetic order is favored over $\sqrt{3}\times\sqrt{3}$ for $0\le \Delta <\Delta_c$ and vice versa for $\Delta_c < \Delta \le 1$. We calculate $\Delta_c$ as a function of the spin quantum number $s$.