Monopoles in Dirac spin liquids II: towards a unifying description of 2D quantum magnetism

The understanding of monopole quantum numbers in Dirac spin liquids provides a unified description of 2D quantum magnetism. In particular, it allows us to naturally account for various orders on both bipartite lattices such as the square and honeycomb lattice as well as the non-bipartite triangular and Kagome lattices. A dichotomy in behavior between the bipartite and non bipartite lattices is traced to the difference in monopole symmetry properties on these two lattices. We characterize universal signatures of the Dirac spin liquid state, including those that result from monopole excitations, which serve as a guide to numerics and to experiments on existing materials. Even when unstable, the Dirac spin liquid unifies multiple seemingly unrelated ordered states, which could help organize the plethora of phases observed in strongly correlated two dimensional materials.