Intermediate and spin-liquid phase of the half-filled honeycomb Hubbard model

We obtain the phase diagram of the half-filled honeycomb Hubbard model with density matrix embedding theory, to address recent controversy at intermediate couplings. We use clusters from 2--12 sites and lattices at the thermodynamic limit. We identify a paramagnetic insulating state, with possible hexagonal cluster order, competitive with the antiferromagnetic phase at intermediate coupling. However, its stability is strongly cluster and lattice size dependent, explaining controversies in earlier work. Our results support the paramagnetic insulator as being a metastable, rather than a true, intermediate phase, in the thermodynamic limit.