title: Magnetic order in the Hubbard model in three dimensions and the crossover to two dimensions.
abstract: Systems of fermions described by the three-dimensional (3D) repulsive Hubbard model on a cubic lattice have recently attracted considerable attention due to their possible experimental realization via cold atoms in an optical lattice. Analytical and numerical results are limited away from half-filling. We study the ground state of the doped system from weak to intermediate interaction strengths within the generalized Hartree-Fock approximation. The exact solution to the self-consistent-field equations in the thermodynamic limit is obtained and the ground state is shown to exhibit antiferromagnetic order and incommensurate spin-density waves (SDW). At low interaction strengths, the SDW has unidirectional character with a leading wavevector along the [100]-direction, and the system is metallic. As the interaction increases, the system undergoes a simultaneous structural and metal-to-insulator transition to a unidirectional SDW state along the [111]-direction, with a different wavelength. We systematically determine the real and momentum space properties of these states. The crossover from 3D to two dimensions (2D) is then studied by varying the inter-plane hopping amplitude, which can be experimentally realized by tuning the distance between a stack of square-lattice layers. Detailed comparisons are made between the exact numerical results and predictions from the pairing model, a variational ansatz based on the pairing of spins in the vicinity of the Fermi surface. Most of the numerical results can be understood quantitatively from the ansatz, which provides a simple picture for the nature of the SDW states.
authors.affiliation: Department of Physics, College of William and Mary, Williamsburg, VA 23187, USA.
authors.forename: Jie
authors.initials: J
authors.lastname: Xu
authors.forename: Simone
authors.initials: S
authors.lastname: Chiesa
authors.forename: Eric J
authors.initials: EJ
authors.lastname: Walter
authors.forename: Shiwei
authors.initials: S
authors.lastname: Zhang
mesh_terms: D000465:Algorithms; D003198:Computer Simulation; D060526:Magnetic Fields; D008670:Metals; D008962:Models, Theoretical; D012542:Scattering, Radiation
chemical_list: D008670:Metals