# Theory of the field-revealed Kitaev spin liquid

## TL;DR

This paper develops a microscopic theory for the field-revealed Kitaev spin liquid, explaining the emergence of non-Abelian anyons and the observed thermal Hall effect in $ ext{RuCl}_3$ under magnetic fields.

## Contribution

It introduces an antiferromagnetic off-diagonal interaction in the Kitaev model, enabling the spin liquid phase to appear between low- and high-field states, and predicts anisotropic effects and non-Abelian anyons.

## Key findings

- A microscopic model capturing the field-revealed Kitaev spin liquid.
- Prediction of a wide regime of non-Abelian anyon spin liquid under perpendicular magnetic fields.
- Strong anisotropy of field effects in the 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.