  The effect of electron-electron interactions on Dirac fermions, and the
possibility of an intervening spin liquid phase between the semi-metal and
antiferromagnetic (AF) regimes, has been a focus of intense quantum simulation
effort over the last five years. We use determinant quantum Monte Carlo (DQMC)
to study the Holstein model on a Honeycomb lattice and explore the role of
electron-phonon interactions on Dirac fermions. We show that they give rise to
charge density wave (CDW) order, and present evidence that this occurs only
above a finite critical interaction strength. We evaluate the temperature for
the transition into the CDW which, unlike the AF transition, can occur at
finite values owing to the discrete nature of the broken symmetry.

Strongly Correlated Electrons