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Keywords:

  • 3D Hubbard model;
  • antiferromagnetic phases;
  • localized magnetic moments

Abstract

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.