Competing orders in Dirac fermions
Correlated Dirac systems are currently one of the most active research areas in condensed matter physics. The topic is experimentally relevant in the context of graphene and other Dirac materials, and theoretically releveant because the corresponding low-energy field theories exhibit remarkable topological properties and are closely related to high-energy physics. We will present exact quantum Monte Carlo results for a model of Dirac fermions in 2+1 dimensions with dynamically generated, anti-commuting SO(3) Néel and Z2 Kekulé mass terms. We will provide evidence for a direct and continuous transition between the Néel and Kekulé phases. The fermions remain gapped across the transition, and our data support an emergent SO(4) symmetry unifying the two order parameters. While this phase transition falls outside the Ginzburg-Landau-Wilson paradigm, the emergent SO(4) invariance permits an interpretation of the transition in terms of deconfined quantum criticality .
 T. Sato, M. Hohenadler, and F. F. Assaad, Phys. Rev. Lett. 119, 197203 (2017).