Projective symmetry group classifications of quantum spin liquids on the simple cubic, body centered cubic, and face centered cubic lattices

We perform extensive classifications of Z₂ quantum spin liquids on the simple cubic, body centered cubic, and face centered cubic lattices using a spin-rotation-invariant fermionic projective symmetry group approach. Taking into account that all three lattices share the same point group O_h, we apply an efficient gauge where the classification for the simple cubic lattice can be partially carried over to the other two lattices. We identify hundreds of projective representations for each of the three lattices, however, when constructing short-range mean-field models for the fermionic partons (spinons) these phases collapse to only very few relevant cases. We finally present self-consistently calculated spinon band dispersions for the face centered cubic lattice up third nearest-neighbor couplings and discuss the relation of a network of symmetry-protected linelike zero modes in reciprocal space with their corresponding projective symmetry group representation.