Possible algebraic spin liquid in half-filled Hubbard model at intermediate U/t

Using large-scale fermion-sign-free projective Determinant Quantum Monte-Carlo (DQMC) method, we study the half-filled Hubbard model on the square lattice with staggered-flux. We calculate the single-particle gap, charge gap, as well as the improved dimensionless estimator of the antiferromagnetic (AF) order parameter, and map out the ground state phase diagram of this model spanned by U/t and staggered-flux. The lattice in our DQMC simulations has 2*L*L sites with largest L$=$28. In the case of $\backslash $pi-flux, finite-size scaling analysis indicates a possible algebraic quantum spin liquid phase between the semi-metal phase at small U/t and the AF phase at large U/t. The algebraic spin liquid occurs in the arrange of 5.4 \textless U/t \textless 5.6. When the staggered-flux is smaller than the critical value of about $\backslash $pi/10, the Fermi velocity in this system is largely anisotropic and it exhibits a direct transition from semi-metal phase to AF phase.