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We study the evolution of the pairing from weak to strong coupling on ahoneycomb lattice by Quantum Monte Carlo. We show numerical evidence of theBCS-BEC crossover as the coupling strength increases on a honeycomb latticewith small fermi surface by measuring a wide range of observables: doubleoccupancy, spin susceptibility, local pair correlation, and kinetic energy.Although at low energy, the model sustains Dirac fermions, we do not findsignificant qualitative difference in the BCS-BEC crossover as compared tothose with an extended Fermi surface, except at weak coupling, BCS regime.

Evolution of pairing from weak to strong coupling on a honeycomb lattice