Metallic Gross-Neveu criticality and superconductivity on the $\mathrm{SO}(3)$ SLAC fermion

Abstract

The realization of Dirac criticality beyond the conventional Gross-Neveu-Yukawa (GNY) paradigm has become a major frontier in condensed matter physics. In this work, we introduce an $\mathrm{SO}(3)$-symmetric bilayer SLAC fermion model with tunable inter-layer interactions that exhibits a rich quantum phase diagram. As the interaction strength increases, the system undergoes two distinct phase transitions. The primary transition is a continuous boundary separating a Dirac semimetal (DSM) from an $\mathrm{SO}(3)$-broken ordered phase. Crucially, this transition evades the standard GNY universality class because the emergent order only gaps out a subset of the itinerant fermions. Using large-scale quantum Monte Carlo (QMC) simulations, we establish that this transition belongs to the Gross-Neveu-$\mathrm{SO}(3)$ universality class with $N=6$ irreducible Dirac cones and precisely extract the corresponding critical exponents. At stronger couplings, a second transition drives the system into an inter-layer $\mathrm{SO}(3)$-symmetric superconducting (SC) state. We provide strong numerical evidence that this transition is first-order. Our study provides new insights into the exploration of Dirac criticality beyond the standard GNY universality class, and also offers a distinct platform for investigating $\mathrm{SO}(3)$-symmetric superconductivity.

10 pages, 6 figures, including Supplemental Material. References and discussion of the strong-coupling phase have been updated to account for the symmetry-degenerate interlayer-coherent and superconducting orders in the N=12 model. A related SLAC-fermion study has also been cited. Numerical results and main conclusions are unchanged