Quantum spin liquids on the diamond lattice

We perform a projective symmetry group classification of spin S = 1/2 symmetric quantum spin liquids with different gauge groups on the diamond lattice. Employing the Abrikosov fermion representation, we obtain 8 SU(2), 62 U(1), and 80 Z(2) algebraic PSGs. Constraining these solutions to mean-field parton Ansatze with short-range amplitudes, the classification reduces to only 2 SU(2), 7 U(1), and 8 Z(2) distinctly realizable phases. We obtain both the singlet and triplet fields for all Ansatze, discuss the spinon dispersions, and present the dynamical spin structure factors within a self-consistent treatment of the Heisenberg Hamiltonian with up to third nearest neighbor couplings. Interestingly, we find that a zero-flux SU(2) state and some descendent U( 1) and Z(2) states host robust gapless nodal loops in their dispersion spectrum, owing their stability at the mean-field level to the projective implementation of rotoinversion and screw symmetries. A nontrivial connection is drawn between one of our U(1) spinon Hamiltonians (belonging to the nonprojective class) and the Fu-Kane-Mele model for a three-dimensional topological insulator on the diamond lattice. We show that Gutzwiller projection of the 0- and pi-flux SU(2) spin liquids generates long-range Neel order.