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.

5 pages, 4 figures + 6.2 pages, 4 figures supplemental, minor changes, accepted version

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• Dynamic fingerprint of fractionalized excitations in single-crystalline Cu${}_3$Zn(OH)${}_6$FBr
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• Ordered ground states of kagome magnets with generic exchange anisotropy
• Classical ground states of spin lattices
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• Color ice states, weathervane modes, and order by disorder in the bilinear-biquadratic pyrochlore Heisenberg antiferromagnet
• Quantum-classical crossover in the spin-1/2 Heisenberg-Kitaev kagome magnet
• Frustration relief and reorientation transition in the kagome-like dolerophanite Cu${}_2$OSO${}_4$
• Absence of long-range order in a general spin-$S$ kagome lattice Ising antiferromagnet
• Exact deconfined gauge structures in the higher-spin Yao-Lee model: a quantum spin-orbital liquid with spin fractionalization and non-Abelian anyons
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• Thermal features of Heisenberg antiferromagnets on edge- versus corner-sharing triangular-based lattices: A message from spin waves
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• Quantum dynamics of frustrated Josephson junction arrays embedded in a transmission line: an effective XX spin chain with long-range interaction
• Demystifying quantum escapism on the honeycomb lattice
• Phase-space networks and connectivity of the kagome antiferromagnet
• Thermal and quantum fluctuations in extended Kitaev-Yao-Lee spin-orbital model
• Programmable order by disorder effect and underlying phases through dipolar quantum simulators