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

## TL;DR

This paper investigates how Hubbard interaction influences edge states in the Rice-Mele model, revealing that repulsive interactions can induce zero-energy edge states and cause their migration between energy gaps.

## Contribution

It demonstrates the novel phenomenon of edge state transmigration between energy gaps driven by Hubbard interaction in the Rice-Mele chain.

## Key findings

- Edge states descend to zero energy at U ≈ 2V
- Edge states reappear at high energy gaps after initial disappearance
- Hubbard interaction causes edge states to migrate between energy gaps

## Abstract

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.