  The spontaneous generation of charge-density-wave order in a Dirac fermion
system via the natural mechanism of electron-phonon coupling is studied in the
framework of the Holstein model on the honeycomb lattice. Using two independent
and unbiased quantum Monte Carlo methods, the phase diagram as a function of
temperature and coupling strength is determined. It features a quantum critical
point as well as a line of thermal critical points. Finite-size scaling appears
consistent with fermionic Gross-Neveu-Ising universality for the quantum phase
transition, and bosonic Ising universality for the thermal phase transition.
The critical temperature has a maximum at intermediate couplings. Our findings
motivate experimental efforts to identify or engineer Dirac systems with
sufficiently strong and tunable electron-phonon coupling.
