Quantum Selection of Order in an $XXZ$ Antiferromagnet on a Kagomé Lattice

Abstract

Selection of the ground state of the kagomé-lattice $XXZ$ antiferromagnet by quantum fluctuations is investigated by combining non-linear spin-wave and real-space perturbation theories. The two methods unanimously favor $\mathbf{q}=0$ over $\sqrt{3}\times \sqrt{3}$ magnetic order in a wide range of the anisotropy parameter $0\le \Delta \le 0.72$. Both approaches are also in an accord on the magnitude of the quantum order-by-disorder effect generated by topologically non-trivial, loop-like spin-flip processes. A tentative $S-\Delta$ phase diagram of the model is proposed.

arXiv comment5 pages, 4 figures + 6.2 pages, 4 figures supplemental, minor changes, accepted version

References in corpus (28)

• Spin Liquid Ground State of the $S=1/2$ Kagome Heisenberg Model
• Fractionalized excitations in the spin liquid state of a kagomé lattice antiferromagnet
• Spin Dynamics of the Spin-1/2 Kagome Lattice Antiferromagnet ZnCu_3(OH)_6Cl_2
• Order versus Disorder in the Quantum Heisenberg Antiferromagnet on the Kagom{é} lattice: an approach through exact spectra analysis
• Gapless spin-liquid phase in the kagome spin-1/2 Heisenberg antiferromagnet
• Ground State of the Kagome Lattice Heisenberg Antiferromagnet
• Symmetry breaking due to Dzyaloshinsky-Moriya interactions in the kagome lattice
• 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
• Spin waves in the Frustrated Kagome Lattice Antiferromagnet KFe3(OH)6(SO4)2
• Physics of low energy singlet states of the Kagome lattice quantum Heisenberg antiferromagnet
• Pinwheel VBS state and triplet excitations in the two-dimensional deformed kagome lattice
• RVB description of the low-energy singlets of the spin 1/2 kagome antiferromagnet
• The Heisenberg antiferromagnet on the kagome lattice with arbitrary spin: A high-order coupled cluster treatment
• A Schwinger-boson approach to the kagome with Dzyaloshinskii-Moriya interactions: phase diagram and dynamical structure factors
• Magnetic Structure and Spin Waves in the Kagomé Jarosite compound $\mathbf{KF}{\mathbf{e}}_3(\mathbf{S}{\mathbf{O}}_4{)}_2(\mathbf{OH}{)}_6$
• Dzyaloshinsky-Moriya interaction in vesignieite: A route to freezing in a quantum kagome antiferromagnet
• Quantum criticality of the kagome antiferromagnet with Dzyaloshinskii-Moriya interactions
• Semi-classical spin dynamics of the antiferromagnetic Heisenberg model on the kagome lattice
• Spin tunneling in the Kagomé antiferromagnet
• Phase transitions in the antiferromagnetic XY model with a kagome lattice
• Degenerate perturbation theory of quantum fluctuations in a pyrochlore antiferromagnet
• Long range order in the classical kagome antiferromagnet: effective Hamiltonian approach
• Quantum dimer model for the spin-1/2 kagome Z2 spin liquid
• Phenomenological Z_2 lattice gauge theory of the spin-liquid state of the kagome Heisenberg antiferromagnet
• XY checkerboard antiferromagnet in external field
• Structure factor of low-energy spin excitations in a S=1/2 kagome antiferromagnet
• Ghost modes and continuum scattering in the dimerized distorted kagome lattice antiferromagnet Rb${}_2$Cu${}_3$SnF${}_{12}$

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