Evolution of quasiparticle edge states with Hubbard interaction in Rice-Mele chain

We study the behaviour of edge states in Rice-Mele model with Hubbard interaction, U , at half-filling using density matrix renormalization group, exact diagonalization and effective charge dynamics in Kumar representation. For a fixed dimerization, $\delta$, and staggered potential, V , we find by increasing U the quasiparticle edge states in the charge gap to come down in energy from V in the absence of Hubbard interaction to zero energy for U $\approx$ 2V . This presents an uncommon case where repulsion leads to zero-energy edge states. Upon increasing U further, the edge state energy starts increasing again until they are lost in the bulk. However, upon increasing U even further, these edge states reappear in the high energy gap. So, with Hubbard interaction, the edge states in Rice-Mele chain transmigrate from the physical charge gap to a high energy gap.