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, t(1), is negligible compared with the second neighbor one, t(2), the system reduces to a collection of Hubbard chains. We find that the 1D character is surprisingly robust as long as t(1) < t(2). 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.