One-dimensional Hubbard model at quarter filling on periodic potentials

TL;DR

This study investigates the ground state properties of a quarter-filled Hubbard chain under periodic potentials, revealing how different potentials induce various charge and spin ordered insulating states, with stability depending on interaction strength.

Contribution

It demonstrates that 2k_F and 4k_F periodic potentials induce distinct insulating states in the Hubbard chain, highlighting the role of interactions and potential type in ground state stability.

Findings

2k_F-periodic magnetic field induces a band insulator with spin gap.

Strong interactions favor 4k_F potential leading to a Mott insulator.

More electrons promote cluster-like charge ordering.

Abstract

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 2k_F- and 4k_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 2k_F-periodic magnetic field, resulting in a band insulator with spin gap. For strong interaction, the 4k_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 2k_F-periodic potential. Adding more electrons, a cluster-like ordering is preferred.