Phase Diagram and Quantum Order by Disorder in the Kitaev $K_1$-$K_2$ Honeycomb Magnet

Abstract

We show that the topological Kitaev spin liquid on the honeycomb lattice is extremely fragile against the second-neighbor Kitaev coupling $K_2$, which has recently been shown to be the dominant perturbation away from the nearest-neighbor model in iridate Na${}_2$IrO${}_3$, and may also play a role in $\alpha$-RuCl${}_3$ and Li${}_2$IrO${}_3$. This coupling naturally explains the zigzag ordering (without introducing unrealistically large longer-range Heisenberg exchange terms) and the special entanglement between real and spin space observed recently in Na${}_2$IrO${}_3$. Moreover, the minimal $K_1$-$K_2$ model that we present here holds the unique property that the classical and quantum phase diagrams and their respective order-by-disorder mechanisms are qualitatively different due to the fundamentally different symmetries of the classical and quantum counterparts.

Published version (9+13 pages)

References in corpus (20)

• Mott Insulators in the Strong Spin-Orbit Coupling Limit: From Heisenberg to a Quantum Compass and Kitaev Models
• $\alpha$-RuCl3: a Spin-Orbit Assisted Mott Insulator on a Honeycomb Lattice
• Magnetic order in $\alpha$-RuCl${}_3$: a honeycomb lattice quantum magnet with strong spin-orbit coupling
• Quantum spin Hall effect in a transition metal oxide Na2IrO3
• Long range magnetic ordering in Na${}_2$IrO${}_3$
• Successive magnetic phase transitions in $\mathbf{\alpha }$-RuCl${}_3$: XY-like frustrated magnet on the honeycomb lattice
• Kitaev magnetism in honeycomb RuCl3 with intermediate spin-orbit coupling
• Kitaev interactions between j=1/2 moments in honeycomb Na2IrO3 are large and ferromagnetic: insights from ab initio quantum chemistry calculations
• Hidden symmetries of the extended Kitaev-Heisenberg model: Implications for honeycomb lattice iridates A2IrO3
• Spin-S Kitaev model: Classical Ground States, Order by Disorder and Exact Correlation Functions
• Importance of anisotropic exchange interactions in honeycomb iridates. Minimal model for zigzag antiferromagnetic order in Na${}_2$IrO${}_3$
• Spin-orbit physics of j=1/2 Mott insulators on the triangular lattice
• Emergent Fermions and Anyons in the Kitaev Model
• Spiral order in the honeycomb iridate Li2IrO3
• Magnetic ordering phenomena of interacting quantum spin Hall models
• A Description of Kitaev's Honeycomb Model with Toric-Code Stabilizers
• Global phase diagram, possible chiral spin liquid and topological superconductivity in the triangular Kitaev-Heisenberg model
• Frustration and Dzyaloshinsky-Moriya anisotropy in the kagome francisites Cu${}_3$Bi(SeO${}_3{)}_2$O${}_2$X
• Effect of nonmagnetic dilution in honeycomb lattice iridates Na${}_2$IrO${}_3$ and Li${}_2$IrO${}_3$
• Intermediate Symmetries In Electronic Systems: Dimensional Reduction, Order Out Of Disorder, Dualities, And Fractionalization

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• Field-induced intermediate ordered phase and anisotropic interlayer interactions in $\alpha$-RuCl${}_3$
• Functional renormalization group for three-dimensional quantum magnetism
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