Quantum spin liquids on the diamond lattice

The diamond lattice has been a promising playground for both classical and quantum spin liquids. Here, the authors conduct a comprehensive symmetry classification of $S$=\textonehalf{} quantum spin liquids with SU(2), U(1), and \ensuremath{\mathbb{Z}}${}_{2}$ gauge fields, and present dynamical spin structure factors within a self-consistent simulation. The authors highlight three discoveries: spinon Ans\"atze with robust gapless nodal loops, topological bands realizing topological insulators, and that Gutzwiller projection of the 0- and $\ensuremath{\pi}$-flux SU(2) spin liquids generates long-range N\'eel order.