Gapless (or "massless") Dirac fermions appear as low-energy excitations in many condensed matter systems of recent interest. They are often weakly interacting, as famously in graphene, but at stronger interactions they can also acquire a gap ("mass") and exhibit many ordered ground states by going through phase transitions at which gapless Dirac fermions play a crucial role. Prime example of this occurs in the Hubbard model on honeycomb lattice at half filling, which suffers a "relativistic Mott transition" from gapless semimetal to gapped insulator, believed to be observed recently in twisted multilayers. I will discuss the recent attempt of unification of all order parameters for Dirac systems in two dimensions based on large but somewhat hidden orthogonal symmetry of free Dirac fermions. Interestingly, the unique interacting field theory that respects such an orthogonal symmetry turns out to be equivalent to the celebrated Gross-Neveu model. I will argue that, in spite of recently turning 50, this model still has a large, unexplored, and surprisingly interesting region of its coupling constant. Recent analytical and numerical results relevant to this "dark side" of the Gross-Neveu model will be presented.
Igor Herbut is a professor of theoretical physics at Simon Fraser University in Burnaby, British Columbia. After receiving his Ph.D. From the Johns Hopkins University in Baltimore, he spent the next three years as a Killam postdoctoral fellow at the University of British Columbia. His interests lay in field theories of condensed matter, and include quantum phase transitions, unconventional superconductivity, and unusual physics of graphene and other topological semimetals in two and three dimensions. He is an author of a graduate textbook on theory of phase transitions and critical phenomena for the Cambridge University Press, a Fellow of the American Physical Society, and a member of the editorial board of the Physical Review B. For his work on interacting Dirac systems he was awarded the Marko Jaric Award for 2017, and the Dresden Physics Prize of the Max Planck Institute and the Technical University Dresden for 2025.