Topological bound states in interacting Su-Schrieffer-Heeger rings

TL;DR

This paper investigates two-particle topological bound states in an interacting SSH chain, revealing new edge states localized in the relative coordinate space, which are distinct from single-particle states and depend on nearest-neighbor interactions.

Contribution

It introduces a novel analysis of two-particle topological states in an SSH model with NN interactions, highlighting their many-body nature and dependence on interaction type.

Findings

Identification of in-gap topological bound states localized at relative coordinate edges.

Presence of additional doublon bands in the energy spectrum.

Topological states are specific to NN interactions, not Hubbard interactions.

Abstract

We study two-particle states in a Su-Shrieffer-Heeger (SSH) chain with periodic boundary conditions and nearest-neighbor (NN) interactions. The system is mapped into a problem of a single particle in a two-dimensional (2D) SSH lattice with potential walls along specific edges. The 2D SSH model has a trivial Chern number but a non-trivial Zak's phase, the one-dimensional (1D) topological invariant, along specific directions of the lattice, which allow for the presence of topological edge states. Using center-of-mass and relative coordinates, we calculate the energy spectrum of these two-body states for strong interactions and find that, aside from the expected appearance of doublon bands, two extra in-gap bands are present. These are identified as bands of topological states localized at the edges of the internal coordinate, the relative distance between the two particles. As such, the topological states reported here are intrinsically many-body in what concerns their real space manifestation, having no counterpart in single-particle states derived from effective models. Finally, we compare the effect of Hubbard interactions with that of NN interactions to show how the presence of the topological bound states is specific to the latter case.