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 signals for phase separation. Upon doping, the system separates into one phase of density $n=1$ (hole free) and the other at density $n_c$ $\left(\sim 0.9\right)$. The long-range antiferromagnetic order is coupled to this process and is lost below $n_c$.