Theory of the field-revealed Kitaev spin liquid

Elementary excitations in highly entangled states such as quantum spin liquids may exhibit exotic statistics, different from those obeyed by fundamental bosons and fermions. Excitations called non-Abelian anyons are predicted to exist in a Kitaev spin liquid - the ground state of an exactly solvable model proposed by Kitaev almost a decade ago. A smoking-gun signature of such non-Abelian anyons, namely a half-integer quantized thermal Hall conductivity, was recently reported in $\alpha$-RuCl$_3$. While fascinating, a microscopic theory for this phenomenon in $\alpha$-RuCl$_3$ remains elusive because the pure Kitaev phase cannot capture these anyons appearing in an intermediate magnetic field. Here we present a microscopic theory of the Kitaev spin liquid emerging between the low- and high-field states. Essential to this result is an antiferromagnetic off-diagonal symmetric interaction that permits the Kitaev spin liquid to protrude from the pure ferromagnetic Kitaev limit under a magnetic field. This generic model captures a field-revealed Kitaev spin liquid, and displays strong anisotropy of field effects. A wide regime of non-Abelian anyon Kitaev spin liquid is predicted when the magnetic field is perpendicular to the honeycomb plane.