Quantitative analysis of interaction effects in generalized Aubry-And\'re-Harper models

TL;DR

This paper analyzes how two-particle interactions affect the topological properties and boundary phenomena in generalized Aubry-André-Harper models, revealing renormalization of band gaps and the emergence of effective edge states.

Contribution

It provides a detailed quantitative study of interaction effects on topological features in generalized 1D models, extending previous work to more complex unit cells.

Findings

Single-particle band gaps are renormalized by interactions.

Interaction-induced effective edge states appear near boundaries.

Boundary charge characteristics remain unaffected by interactions.

Abstract

We present a quantitative analysis of two-particle interaction effects in generalized, one-dimensional Aubry-Andr\'e-Harper models with the Fermi energy placed in one of the band gaps. We investigate systems with periodic as well as open boundary conditions; for the latter focusing on the number of edge states and the boundary charge. Both these observables are important for the classification of noninteracting topological systems. In our first class of models the unit cell structure stems from periodically modulated single-particle parameters. In the second it results from the spatial modulation of the two-particle interaction. For both types of models, we find that the single-particle band gaps are renormalized by the interaction in accordance with expectations employing general field theoretical arguments. While interaction induced effective edge states can be found in the local single-particle spectral function close to a boundary, the characteristics of the boundary charge are not modified by the interaction. This indicates that our results for the Rice-Mele and Su-Schriefer-Heeger model [Phys. Rev. B 102, 085122 (2020)] are generic and can be found in lattice models with more complex unit cells as well.