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 16x16, the results show signals for phase separation. Upon doping, the system separates into one phase of density n=1 (hole free) and the other at density n(c) (similar to 0.9). The long-range antiferromagnetic order is coupled to this process and is lost below n(c).