Interaction-controlled localization in one-dimensional chain: From edges to domain walls

TL;DR

This study uses a Hartree-Fock mean-field approach to explore how on-site and extended Hubbard interactions influence edge modes and localized states in a half-filled SSH chain, revealing a ratio-dependent localization mechanism.

Contribution

It uncovers the interaction-driven origin of localized states in a 1D chain, showing how the ratio of extended to on-site interactions controls edge and domain wall modes.

Findings

Localization of bound states depends on the ratio 2V/U.

Edge spin-density-wave modes occur for U>2V.

Mid-chain charge-density-wave domain walls occur for U<2V.

Abstract

Using Hartree-Fock mean-field approach, we study the role of on-site ($U$) and extended ($V$) Hubbard interactions on the existence and evolution of edge modes in a half-filled Su-Schrieffer-Heeger (SSH) chain. We analyze the energy spectrum, local probability amplitudes, and site-resolved charge and spin density profiles across topological, critical, and trivial hopping regimes. We find that the localization of bound states is controlled by the ratio $2V/U$, with edge spin-density-wave modes for $U>2V$ and mid-chain charge-density-wave domain walls for $U<2V$, independent of band topology. These results establish the correlation-driven origin of localized states in finite one-dimensional chains.