Magnetic (2kF) and electronic (4kF) Peierls transitions from a Hubbard Hamiltonian extended with intersite-dependent transfer

We report a model calculation with an intersite-dependent Hubbard Hamiltonian, showing that the well-known Peierls transition has a $2k_F$ and a $4k_F$ component when the intrasite Coulomb repulsion $U$ is less than the transfer integral $t$. At higher values of $U$ the two components are split and each forms a proper phase transition; the electronic Peierls transition ($4k_F$) remaining at about the same temperature while the magnetic Peierls transition ($2k_F$) is driven towards lower temperatures as $U$ increases. For lower temperatures and lower $U$ a new phase transition occurs, leading from a mixed ($2k_F+4\mathrm{}{k}_F$) phase to a pure $2k_F$ phase. The calculation was performed for two electrons distributed over four sites, but group-theoretical arguments are put forward to show that one may expect an infinitely long chain with a quarter-filled band to show the same behavior.