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Explore a unified theoretical framework for understanding Dirac fermions in 2+1 dimensional condensed matter systems through this 35-minute conference talk. Delve into the SO(8) symmetry underlying these systems and examine how weakly interacting Dirac fermions, such as those found in graphene, can exhibit various ordered ground states under intermediate interactions via continuous phase transitions. Learn about the celebrated Gross-Neveu model with general O(M) symmetry and its well-understood O(M) symmetry-preserving transitions for one interaction coupling sign. Discover a previously unsuspected transition for the opposite coupling sign where O(M) spontaneously breaks to O(M/2) x O(M/2), and investigate the complex universality class problem involving second-rank real tensor order parameters coupled to relativistic fermions. Gain insights into the theoretical foundations of quantum phase transitions in low-dimensional fermionic systems and their applications to contemporary condensed matter physics research.
