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

Abstract

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 π−flux state of SU(4) spin system, and the π−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 π−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 1/N 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.

Stability ofSU(Nc)QCD3Goldman1, Mulligan2 2016Phys. Rev. D4140View full textAdd to dashboardCite

“…(3) is valid to O(1/N f ) [24]; consequently, any solution N F fsignifying the critical number of flavors for which a flow from QCD3 to a massive phase is possible -should be understood to be an estimate valid within the 1/N f expansion. For SU (2) and SU (3) gauge groups, we find N F f (2) ≈ 7 and N F f (3) ≈ 12, in close agreement with previous studies of QCD3 via the 1/N f expansion [2,4]. N F f (and the estimates for the critical number of flavors obtained earlier via the 1/N f expansion [2,4]) is roughly half the value of N crit f that we find using the -expansion in Eq.…”

“…For SU (2) and SU (3) gauge groups, we find N F f (2) ≈ 7 and N F f (3) ≈ 12, in close agreement with previous studies of QCD3 via the 1/N f expansion [2,4]. N F f (and the estimates for the critical number of flavors obtained earlier via the 1/N f expansion [2,4]) is roughly half the value of N crit f that we find using the -expansion in Eq. (2) extrapolated to = 1.…”

“…A solution to the Schwinger-Dyson equations suggests that the theory is driven into a phase in which the fermions acquire a mass at N f = 128 3π 2 N 2 c −1 Nc [2]. For QCD3 with gauge group SU(2), a theory which appears in the study of algebraic spin liquids and theories for high-temperature superconductivity [3], [4] estimates that a particular linear combination of four-fermion operators becomes relevant when N f < 6. While the 1/N f expansion directly accesses three dimensions, the -expansion provides a complementary estimate valid for N f ∼ O(1).…”

Scaling dimensions in QED3 from the ϵ-expansion

“…In fact, the operators with the lowest UV dimension that are singlets under the symmetries of the theory are fourfermion operators. If for small N f they are dangerously irrelevant, i.e., their anomalous dimension is large enough for them to flow to relevant operators in the IR, they may trigger the aforementioned transition [7,27,28]. 1 The one-loop result of ref.…”

“…For large N f the theory flows in the IR to an interacting conformal field theory (CFT) that enjoys the same parity and global symmetry. The CFT observables are then amenable to perturbation theory in 1/N f ; this has been done for scaling dimensions [1][2][3][4][5][6][7][8][9][10][11], two-point functions of conserved currents [12][13][14], and the free energy [15]. The IR fixed point is expected to persist beyond this large-N f regime, but not much is known about it.…”