Quantum critical behavior of the Gross-Neveu-SO(3) universality class: 4−<i>ε</i> expansion, 1/<i>N</i> expansion, and functional renormalization group

The Gross-Neveu-SO(3) universality class describes a quantum critical point between a Dirac semimetal and a phase with long-range order, in which the fermion spectrum is only partially gapped out. Such a quantum critical point has recently been predicted to be realizable in two-dimensional spin-orbital magnets with strong exchange frustration. In this talk, I shall report on our work characterizing the quantum critical behavior of the Gross-Neveu-SO(3) universality class from three complementary field-theoretical approaches: three-loop ε expansion around the upper critical space-time dimension of four, second-order large-N expansion (partly even at third order), as well as functional renormalization group in the local potential approximation.