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We study the evolution of the pairing from weak to strong coupling on a honeycomb lattice by quantum Monte Carlo. We show numerical evidence of the BCS-Bose-Einstein condensation (BEC) crossover as the coupling strength increases on a honeycomb lattice with small Fermi surface by measuring a wide range of observables: double occupancy, spin susceptibility, local pair correlation, and kinetic energy. Although at low energy, the model sustains Dirac fermions, we do not find significant qualitative difference in the BCS-BEC crossover as compared to those with an extended Fermi surface, except at weak-coupling, BCS regime. © 2009 The American Physical Society.

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Physical Review B - Condensed Matter and Materials Physics