Novel Criticality of Dirac Fermions from Lattice Symmetry Breaking

We consider the role of spontaneous lattice symmetry breaking in strongly interacting two dimensional Dirac systems. The fermion induced quantum (multi-)criticality is described by Dirac fermions coupled to a dynamical order parameter that is composed of mass and emergent gauge fields. This is illustrated for the example of translational symmetry breaking due to charge-density wave order on the honeycomb lattice. Using a renormalization-group analysis we find that the putative emergent Lorentz invariance is violated. Finally, we identify that topological phase transitions are well described by this effective field theory.