Magnetic and charge orders in the ground state of the 2D repulsive Hubbard model

We systematically study the ground state of the two-dimensional repulsive Hubbard model as a function of doping and interaction strengths, using the auxiliary field quantum Monte-Carlo (AFQMC) method combined with a self-consistent constraint to control the sign problem. We focus on the spin and charge correlations, applying pinning fields to break translational symmetry and computing the spin and charge densities to probe the emergence of long-range order and collective modes. A phase diagram of spin-density waves is obtained. The effect of next-nearest-neighbor hopping is examined. The relation between the magnetic and pairing correlations will be discussed.