Phase transition from superconductivity to phase separation

We study the evolution of one-body propagator from superconducting state to a phase separated state of a spin-less fermion model with nearest neighboring attraction V. Our sign-free determinant quantum Monte Carlo calculations give two phases of distinct characteristics. Under weak attraction, the system is in a superconducting state displaying a superconducting gap in the weakly dressed dispersion. Under strong attraction, the system is in a phase separated state in which most particles clustered together, resulting in a strong binding energy 4V in the spectral function. As the attraction decreases near a critical value, the cluster begins to dissolve and charge 2e bosons start to emerge. We further investigate the phase transition between these two distinct quantum states of matter.