One-dimensional Hubbard model at quarter filling on periodic potentials

Using the Hubbard chain at quarter filling as a model system, we study the ground state properties of highly doped antiferromagnets. In particular, the Hubbard chain at quarter filling is unstable against $2{k}_{F}$- and $4{k}_{F}$-periodic potentials, leading to a large variety of charge and spin ordered ground states. Employing the density matrix renormalization group method, we compare the energy gain of the ground state induced by different periodic potentials. For interacting systems the lowest energy is found for a $2{k}_{F}$-periodic magnetic field, resulting in a band insulator with spin gap. For strong interaction, the $4{k}_{F}$-periodic potential leads to a half-filled Heisenberg chain and thus to a Mott insulating state without spin gap. This ground state is more stable than the band insulating state caused by any non-magnetic $2{k}_{F}$-periodic potential. Adding more electrons, a cluster-like ordering is preferred.