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 $s$.

arXiv comment6 pages. 4 figures

References in corpus (50)

• Many-Body Physics with Ultracold Gases
• Spin Liquid Ground State of the $S=1/2$ Kagome Heisenberg Model
• First excitations of the spin 1/2 Heisenberg antiferromagnet on the kagomé lattice
• Engineering Ising-XY spin models in a triangular lattice via tunable artificial gauge fields
• Gapless spin-liquid phase in the kagome spin-1/2 Heisenberg antiferromagnet
• Ground State of the Kagome Lattice Heisenberg Antiferromagnet
• Quantum phase transition induced by Dzyaloshinskii-Moriya in the kagome antiferromagnet
• Dzyaloshinsky-Moriya Anisotropy in the Spin-1/2 Kagomé Compound ZnCu${}_3$(OH)${}_6$Cl${}_2$
• Frustrated antiferromagnets with entanglement renormalization: ground state of the spin-1/2 Heisenberg model on a kagome lattice
• 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
• Z2 spin liquid in S=1/2 Heisenberg model on Kagome lattice: A projective symmetry group study of Schwinger-fermion mean-field states
• Tensor renormalization of quantum many-body systems using projected entangled simplex states
• Numerical-Diagonalization Study of Spin Gap Issue of the Kagome Lattice Heisenberg Antiferromagnet
• Ground-State Energy and Spin Gap of Spin-1/2 Kagome Heisenberg Antiferromagnetic Clusters: Large Scale Exact Diagonalization Results
• Quantum $J_1$--$J_2$ antiferromagnet on the stacked square lattice: Influence of the interlayer coupling on the ground-state magnetic ordering
• An efficient implementation of high-order coupled-cluster techniques applied to quantum magnets
• Low energy excitations of the kagome antiferromagnet and the spin gap issue
• The Heisenberg antiferromagnet on the kagome lattice with arbitrary spin: A high-order coupled cluster treatment
• 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
• Less than 50% sublattice polarization in an insulating S=3/2 kagome' antiferromagnet at low T
• Renormalization group analysis of competing quantum phases in the J1-J2 Heisenberg model on the kagome lattice
• High-Order Coupled Cluster Method Study of Frustrated and Unfrustrated Quantum Magnets in External Magnetic Fields
• Quantum Phases of the Planar Antiferromagnetic J_1-J_2-J_3 Heisenberg-Model
• High-Order Coupled Cluster Method Calculations for the Ground- and Excited-State Properties of the Spin-Half XXZ Model
• 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 spin-1/2 J1-J2 Heisenberg ferromagnet on the square lattice: Exact diagonalization and Coupled-Cluster study
• The frustrated Heisenberg antiferromagnet on the honeycomb lattice: A candidate for deconfined quantum criticality
• Dzyaloshinsky-Moriya interaction in vesignieite: A route to freezing in a quantum kagome antiferromagnet
• The quantum $J_1$--$J_1^{\prime }$--$J_2$ spin-1 Heisenberg model: Influence of the interchain coupling on the ground-state magnetic ordering in 2D
• Numerical Contractor Renormalization Method for Quantum Spin Models
• Coupled Cluster Method Calculations Of Quantum Magnets With Spins Of General Spin Quantum Number
• Direct calculation of the spin stiffness on square, triangular and cubic lattices using the coupled cluster method
• Phase transitions in the antiferromagnetic XY model with a kagome lattice
• 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
• Resonating color state and emergent chromodynamics in the kagome antiferromagnet
• Magnetic phases of the mixed-spin $J_1-J_2$ Heisenberg model on a square lattice
• Spin-1/2 Heisenberg antiferromagnet on an anisotropic kagome lattice
• Long range order in the classical kagome antiferromagnet: effective Hamiltonian approach
• 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
• Quantum dimer model for the spin-1/2 kagome Z2 spin liquid
• Large Negative Quantum Renormalization of Excitation Energies in the Spin-1/2 Kagome Lattice Antiferromagnet Cs${}_2$Cu${}_3$SnF${}_{12}$
• Magnetic order in a spin-1/2 interpolating kagome-square Heisenberg antiferromagnet
• Magnetic order in spin-1 and spin-3/2 interpolating square-triangle Heisenberg antiferromagnets
• Ab Initio Simulation of the Nodal Surfaces of Heisenberg Antiferromagnets
• A frustrated spin-1/2 Heisenberg antiferromagnet on a chevron-square lattice

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• The route to magnetic order in the spin-$1/2$ kagome Heisenberg antiferromagnet: The role of interlayer coupling
• Structure Factors of the Kagome-Lattice Heisenberg antiferromagnets at finite temperatures
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• The Spin-Half {\it XXZ} Antiferromagnet on the Square Lattice Revisited: A High-Order Coupled Cluster Treatment
• Ordered ground states of kagome magnets with generic exchange anisotropy
• Non-Coplanar Model States in Quantum Magnetism Applications of the High-Order Coupled Cluster Method
• Variational Monte Carlo study of gapless spin liquid in the spin-$1/2$ XXZ antiferromagnetic model on the kagome lattice
• Loop-gas description of the localized-magnon states on the kagome lattice with open boundary conditions
• Absence of long-range order in a general spin-$S$ kagome lattice Ising antiferromagnet
• Coupled Cluster Treatment of the Alternating Bond Diamond Chain
• Correspondence between excited energy eigenstates and local minima of energy landscape in quantum spin systems
• Cheaper and more noise-resilient quantum state preparation using eigenvector continuation
• Emergence of magnetic long-range order in kagome quantum antiferromagnets