Attractive Hubbard model on a honeycomb lattice: Quantum Monte Carlo study

We study the attractive fermionic Hubbard model on a honeycomb lattice using determinantal quantum Monte Carlo simulations. By increasing the interaction strength $U$ (relative to the hopping parameter $t$) at half filling and zero temperature, the system undergoes a quantum phase transition at $5.0l{U}_{c}/tl5.1$ from a semimetal to a phase displaying simultaneously superfluid behavior and density order. Doping away from half filling, and increasing the interaction strength at finite but low temperature $T$, the system always appears to be a superfluid exhibiting a crossover between a BCS and a molecular regime. These different regimes are analyzed by studying the spectral function. The formation of pairs and the emergence of phase coherence throughout the sample are studied as $U$ is increased and $T$ is lowered.