  We investigate ground state properties of the half-filled staggered-flux
Hubbard model on a square lattice. Energy gaps to charge and spin excitations
and magnetic as well as dimer orders are calculated as a function of
interaction strength $U/t$ by means of constrained-path quantum Monte Carlo
method. It is found that the system is a semi-metal at $U/t\lesssim 5.6$ and a
Mott insulator with long-range antiferromagnetic order at $U/t \gtrsim 6.6$. In
the range $5.6\lesssim U/t\lesssim 6.6$, the ground state is an correlated
insulator where both magnetic and dimer orders are absent. Furthermore, spin
excitation in the intermediate phase appears to be gapless, and the measured
spin-spin correlation function exhibits power-law decaying behavior. The data
suggest that the non-magnetic ground state is a possible candidate for the
putative algebraic spin liquid.
