Dimensional reduction and odd-frequency pairing of the checkerboard-lattice hubbard model at 1/4-filling

The ferromagnetism of the checkerboard-lattice Hubbard model at quarter filling is one of the few exact ferromagnetic ground states known in the family of Hubbard models. When the nearest neighbor hopping, t₁, is negligible compared with the second neighbor one, t₂, the system reduces to a collection of Hubbard chains. We find that the 1D character is surprisingly robust as long as t₁ < t₂. This phenomenon of dimensional reduction due to the geometrical frustration leads to peculiar magnetic orders with 1D character for intermediate U and is responsible for odd-frequency superconducting states close to the magnetic boundary.