# Novel criticality of Dirac fermions from lattice symmetry breaking

## TL;DR

This paper investigates how spontaneous lattice symmetry breaking influences the critical behavior of strongly interacting 2D Dirac fermions, revealing violations of emergent Lorentz invariance and describing topological phase transitions.

## Contribution

It introduces a new effective field theory for Dirac fermions coupled to order parameters, highlighting the impact of lattice symmetry breaking on criticality and Lorentz invariance.

## Key findings

- Emergent Lorentz invariance is violated in the studied system.
- Topological phase transitions are effectively described by the proposed theory.
- Lattice symmetry breaking significantly alters the critical behavior of Dirac fermions.

## Abstract

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.

---
Source: https://tomesphere.com/paper/1906.03892