Spin and charge order in doped Hubbard model: long-wavelength collective modes

Determining the ground state properties of the two-dimensional Hubbard model has remained an outstanding problem. Applying recent advances in constrained path auxiliary-field quantum Monte Carlo techniques and simulating large rectangular periodic lattices, we calculate the long-range spin and charge correlations in the ground state as a function of doping. At intermediate interaction strengths, an incommensurate spin density wave (SDW) state is found, with antiferromagnetic order and essentially homogeneous charge correlation. The wavelength of the collective mode decreases with doping, as does its magnitude. The SDW order vanishes beyond a critical doping. As the interaction is increased, the holes go from a wave-like to a particle-like state, and charge ordering develops which eventually evolves into stripe-like states.