Projective symmetry group classification of chiral mathbb{Z}₂ spin liquids on the pyrochlore lattice: application to the spin-1/2 XXZ Heisenberg model

We give a complete classification of fully symmetric as well as chiral mathbb{Z}₂ quantum spin liquids on the pyrochlore lattice using a projective symmetry group analysis of Schwinger boson mean-field states. We find 50 independent ansätze, including the 12 fully symmetric nearest-neighbor mathbb{Z}₂ spin liquids that have been classified by Liu et al. [https://journals.aps.org/prb/abstract/10.1103/PhysRevB.100.075125]. For each class we specify the most general symmetry-allowed mean-field Hamiltonian. Additionally, we test the properties of a subset of the spin liquid ansätze by solving the mean-field equations for the spin-1/2 XXZ model near the antiferromagnetic Heisenberg point. We find four chiral spin liquids that break the screw symmetry of the lattice modulo time reversal symmetry. These states have a different symmetry than the previously studied monopole flux state and their unique characteristic is a fracπ{3} flux enclosed by every rhombus of the lattice.