  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.
