Algebraic spin liquid as the mother of many competing orders

We study the properties of a class of two-dimensional interacting critical states-dubbed algebraic spin liquids-that can arise in two-dimensional quantum magnets. A particular example that we focus on is the staggered flux spin liquid, which plays a key role in some theories of underdoped cuprate superconductors. We show that the low-energy theory of such states has much higher symmetry than the underlying microscopic spin system. This symmetry has remarkable consequences, leading in particular to the unification of a number of seemingly unrelated competing orders. The correlations of these orders-including, in the staggered flux state, the Neel vector, and the order parameter for the columnar and box valence-bond solid states-all exhibit the same slow power-law decay. Implications for experiments in the pseudogap regime of the cuprates and for numerical calculations on model systems are discussed.