Quantum Monte Carlo study of the Hubbard model on a square lattice in the ground state is reported. For the on-site interaction U=4 scaled by the transfer, the charge excitation gap at the half-filling is estimated to be δ, = 0.58±0.08. Near half-filling, the charge compressibility k follows the form k∝ δ-1 for the doping concentration δ, indicating a divergent behavior as the system approaches half-filling, while k = 0 at the half-filling. The incommensurate spin correlation length ∊ scales as [formula omitted].
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