Title: Dirac and Chiral Quantum Spin Liquids on the Honeycomb Lattice in a Magnetic Field,
Abstract: Motivated by recent experimental observations in $\alpha$-RuCl$_3$, we study
the $K$-$\Gamma$ model on the honeycomb lattice in an external magnetic field.
By a slave-particle representation and Variational Monte Carlo calculations, we
reproduce the phase transition from zigzag magnetic order to a field-induced
disordered phase. The nature of this state depends crucially on the field
orientation. For particular field directions in the honeycomb plane, we find a
gapless Dirac spin liquid, in agreement with recent experiments on
$\alpha$-RuCl$_3$. For a range of out-of-plane fields, we predict the existence
of a Kalmeyer-Laughlin-type chiral spin liquid, which would show an
integer-quantized thermal Hall effect.