Kitaev spin-1/2 materials on the honeycomb lattice are a class of candidate materials that can potentially be used for realizing topological quantum computations. Existing Kitaev materials exhibit magnetic orders at low temperatures, including zigzag, counter-rotating spiral, and triple-Q orders, among others. In this talk, I will discuss our recent progress in understanding the magnetic orders in Kitaev materials through a coupled-chain analysis.

In the first part of the talk, I will start with a single Kitaev-Gamma spin-1/2 chain and show that an extended gapless phase with emergent SU(2)1 symmetry exists. Using this as a starting point, we studied the Kitaev-Heisenberg-Gamma chain and found a gapless phase and a ferromagnetic phase. In the second part, I will describe how we extended these 1D findings to 2D by connecting 1D chains and using a self-consistent mean field approach. This method successfully explains the zigzag order in alpha-RuCl3 and Na2IrO3, and spiral orders in alpha-Li2IrO3, based on a nearest-neighbor model without needing more complex interactions.

[1] W. Yang, A. Nocera, T. Tummuru, H.-Y. Kee, I. Affleck, Phys. Rev. Lett. 124, 147205 (2020).

[2] W. Yang, A. Nocera, I. Affleck, Phys. Rev. Research 2, 033268 (2020).

[3] W. Yang, A. Nocera, C. Xu, H.-Y. Kee, I. Affleck, arXiv:2207.02188 (2022).