Heisenberg-Kitaev physics in magnetic fields

Kitaev's bond-anisotropic spin model on the honeycomb lattice describes an exactly solvable quantum spin liquid with emergent gauge fields and fractionalized excitations. By now, a number of honeycomb-lattice magnets have been proposed to host sizeable Kitaev interactions, driven by strong spin-orbit coupling, among them Na₂IrO₃, α-Li₂IrO₃, and α-RuCl₃. Given the strong spin anisotropies, their response to applied magnetic fields is particularly rich. In this talk, I will describe the behavior of the relevant Heisenberg-Kitaev models and their extensions in applied field, with focus on field-induced exotic phases and their experimental signatures. I will also discuss phases of the hyperhoneycomb-lattice extended Kitaev models relevant for β-Li₂IrO₃ and a mapping connecting them to their two-dimensional counterparts.