Multinode quantum spin liquids on the honeycomb lattice

Recently it was realized that the zigzag magnetic order in Kitaev materials can be stabilized by small negative off-diagonal interactions called the Gamma' terms. To fully understand the effect of the Gamma' interactions, we investigate the quantum K-Gamma-Gamma' model on the honeycomb lattice using the variational Monte Carlo method. Two multinode Z(2) quantum spin liquids (QSLs) are found at Gamma' > 0, one of which is the previously found proximate Kitaev spin liquid called the PKSL14 state, which shares the same projective symmetry group (PSG) with the Kitaev spin liquid. A remarkable result is that a pi-flux state with a distinct PSG appears at larger Gamma'. The pi-flux state is characterized by an enhanced periodic structure in the spinon dispersion in the original Brillouin zone (BZ), which is experimentally observable. Interestingly, two PKSL8 states are competing with the pi-flux state and one of them can be stabilized by six-spin ring-exchange interactions. The physical properties of these nodal QSLs are studied by applying magnetic fields and the results depend on the number of cones. Our study infers that there exist a family of zero-flux QSLs that contain 6n + 2, n is an element of Z Majorana cones and a family of pi-flux QSLs containing 4(6n + 2) cones in the original BZ. It provides guidelines for experimental realization of non-Kitaev QSLs in relevant materials.