Emergent symmetries in relativistic Quantum Phase Transitions

This work deals with quantum phase transitions in Dirac systems where the symmetries involved play a key role in the nature of the transition and are enlarged at criticality. By using functional renormalization group (FRG) methods, we show that an emergent relativistic symmetry not present at the bare level is a common feature of several different kinds of phase transitions. In three different projects, the interplay of emergent symmetries and universality in critical phenomena are explored through FRG techniques. In the first project, we studied the relation between discrete symmetry breaking and the emergence of two diverging length scales with their respective critical exponents. A second project explored the relation between multicritical points where two adjacent symmetry-breaking phases are compatible and the possibility of a continuous, order-to-order transition. The third and final project was concerned with the persistence of chiral symmetry in three-dimensional quantum electrodynamics - here seen as an effective description of different condensed matter systems - for the lowest possible number of fermion flavours, as well as with a dual description that has the potential to provide exact results for this strongly correlated theory