Spatially inhomogeneous phase in the two-dimensional repulsive Hubbard   model
  Using recent advances in auxiliary-field quantum Monte Carlo techniques and the phaseless approximation to control the sign/phase problem, we determine the equation of state in the ground state of the two-dimensional repulsive single-band Hubbard model at intermediate interactions. Shell effects are eliminated and finite-size effects are greatly reduced by boundary condition integration. Spin-spin correlation functions and structure factors are also calculated. In lattice sizes up to $16\times 16$, the results show signal for phase-separation. Upon doping, the system separates into one phase of density $n=1$ (hole-free) and the other at density $n_c$ ($\sim 0.9$). The long-range antiferromagnetic order is coupled to this process, and is lost below $n_c$. 
Chia-Chen Chang and Shiwei Zhang