Renormalization group studies on four-fermion interaction instabilities on algebraic spin liquids

We study the instabilities caused by four-fermion interactions on algebraic spin liquids. Renormalization group (RG) is used for three types of previously proposed spin liquids on the square lattice: the staggered flux state of SU(2) spin system, the pi-flux state of SU(4) spin system, and the pi-flux state of SU(2) spin system. The low-energy field theories of the first two types of spin liquids are QED3 with emerged SU(4) and SU(8) flavor symmetries, the low-energy theory of the pi-flux SU(2) spin liquid is the QCD3 with SU(2) gauge field and emergent Sp(4) [SO(5)] flavor symmetry. Suitable large-N generalization of these spin liquids are discussed, and a systematic UN expansion is applied to the RG calculations. The most relevant four-fermion perturbations are identified, and the possible phases driven by relevant perturbations are discussed.