Characterizing Extended Kitaev Models Under a Magnetic Field*

The Kitaev honeycomb model and its extensions across dimensions, spin length, and additional interactions has been the subject of intense theoretical research. Initially an academic problem, the extended Kitaev model has found relevance in a large number of material candidates including the promising honeycomb α-RuCl₃.

Recently there has been interest in low-dimensional analogues of the extended Kitaev model, as they exhibit rich phase diagrams with SPTs, chiral order, higher-rank magnetism, and Luttinger liquids. In addition to being more amenable to numerical study, their phase diagrams have some remarkable similarities to the 2D honeycomb model and may provide further insights into the nature of the 2D phases.

Aligned with this program, in this talk I summarize recent numerical and analytical work on these extended Kitaev models. After discussing the anisotropic spin-S Kitaev chain, I go on to talk about quasi-1D Kitaev systems under magnetic fields, as well as a difficult corner of the honeycomb phase diagram thought

to be relevant for α-RuCl₃. Finally, I discuss a symmetry-based thermodynamic signature of topological phase transitions, applicable to a number of candidate materials.