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

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 $s$.

6 pages. 4 figures

References in corpus (19)

• Many-Body Physics with Ultracold Gases
• Ground State of the Kagome Lattice Heisenberg Antiferromagnet
• Dzyaloshinsky-Moriya Anisotropy in the Spin-1/2 Kagomé Compound ZnCu${}_3$(OH)${}_6$Cl${}_2$
• Quantum phase transition induced by Dzyaloshinskii-Moriya in the kagome antiferromagnet
• Ground-state phases of the spin-1/2 J_1-J_2 Heisenberg antiferromagnet on the square lattice: A high-order coupled cluster treatment
• Valence Bond Solids and Their Quantum Melting in Hard-Core Bosons on the Kagome Lattice
• Spin waves in the Frustrated Kagome Lattice Antiferromagnet KFe3(OH)6(SO4)2
• Numerical-Diagonalization Study of Spin Gap Issue of the Kagome Lattice Heisenberg Antiferromagnet
• Quantum $J_1$--$J_2$ antiferromagnet on the stacked square lattice: Influence of the interlayer coupling on the ground-state magnetic ordering
• Distinct Spin Liquids and their Transitions in Spin-1/2 XXZ Kagome Antiferromagnets
• Quantum Selection of Order in an $XXZ$ Antiferromagnet on a Kagomé Lattice
• Effect of anisotropy on the ground-state magnetic ordering of the spin-half quantum $J_1^{XXZ}$--$J_2^{XXZ}$ model on the square lattice
• The frustrated Heisenberg antiferromagnet on the honeycomb lattice: A candidate for deconfined quantum criticality
• Numerical Contractor Renormalization Method for Quantum Spin Models
• Magnetic order in coupled spin-half and spin-one Heisenberg chains in anisotropic triangular-lattice geometry
• Long-Range Order of the Three-Sublattice Structure in the S = 1 Heisenberg Antiferromagnet on a Spatially Anisotropic Triangular Lattice
• Spin-1/2 Heisenberg antiferromagnet on an anisotropic kagome lattice
• The quantum $J_1$-$J_1^{\prime }$-$J_2$ spin-1/2 Heisenberg model: Influence of the interchain coupling on the ground-state magnetic ordering in 2D
• The frustrated spin-$\frac{1}{2}$ $J_1$--$J_2$ isotropic $XY$ model on the honeycomb lattice

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