Motivated by recent experimental observations in α-RuCl_{3}, we study the K-Γ 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 α-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.
Variational Monte Carlo (VMC) studies of extended Kitaev honeycomb models reveal a series of multinode quantum spin liquids (QSLs). They have an emergent Z 2 gauge structure, a discrete number of symmetry-protected Majorana cones, and form Abelian or non-Abelian chiral spin liquids in applied magnetic fields. The large number of Z 2 projective symmetry groups for spin–orbit-coupled states on the honeycomb lattice suggests that multinode QSLs can be found experimentally in future work on proximate Kitaev materials.
By including a material-relevant off-diagonal interaction called the $\mathrm{\ensuremath{\Gamma}}$ term into the Kitaev model and introducing spatial anisotropy in the interaction strength on the honeycomb lattice, we obtain a series of nodal
Z2 quantum spin liquids (QSLs) from the parton approach. These QSLs share the same projective symmetry group and are characterized by certain numbers of symmetry-protected Majorana cones in their low-energy excitation spectrum. We illustrate that the physical properties of the QSLs are dependent on the information of the cones. Using the $\mathbit{k}\ifmmode\cdot\else\textperiodcentered\fi{}\mathbit{p}$ method, we analyze the chirality of every cone with respect to mass generating perturbations. Especially, for an applied external magnetic field, we provide the maximum-mass field orientation for every cone. Thus, for arbitrarily oriented weak magnetic fields, we can immediately read out the Chern number of the system and the properties of the resultant chiral spin liquids. The new gapless QSLs predicted in our phase diagrams are promising to be realized experimentally by exerting uniaxial pressure to tune the anisotropy of the interaction strength. We further show that all these QSLs can be distinguished by measurable quantities. Based on the study of these QSL phases, we conclude that a complete classification of nodal QSLs with certain symmetry should include not only the projective symmetry groups, but also the information of the cones, i.e., their total number, their chiralities, and the way in which they are symmetry related.