Néel order and the destruction of localized magnetic moments in the crossover from the Mott–Heisenberg to the Slater limit

We study the antiferromagnetic phase of the three‐dimensional (3D) Hubbard model with nearest‐neighbor hopping on a bipartite cubic lattice. We use the quantum SU(2) × U(1) rotor approach that yields a fully self‐consistent treatment of the antiferromagnetic state that respects the symmetry properties of the model and satisfies the Mermin–Wagner theorem. As our theory describes the evolution from a Slater ( U  ≪  t ) to a Mott–Heisenberg ( U  ≫  t ) antiferromagnet, we present the phase diagram of the antiferromagnetic Hubbard model as a function of the crossover parameter U / t .