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

TL;DR

This paper investigates the fragility of the Kitaev spin liquid on the honeycomb lattice under second-neighbor couplings, revealing how these interactions influence magnetic ordering and quantum-classical phase diagram differences.

Contribution

It introduces a minimal $K_1$-$K_2$ model demonstrating the distinct classical and quantum phase diagrams and order-by-disorder mechanisms due to symmetry differences.

Findings

Second-neighbor Kitaev coupling explains zigzag order in Na$_2$IrO$_3$

Classical and quantum phase diagrams differ significantly

Fragility of the Kitaev spin liquid against $K_2$ perturbation

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.