Theory of the field-revealed Kitaev spin liquid

Abstract: 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.