Quantitative analysis of interaction effects in generalized Aubry-André-Harper models

Physical review. B./Physical review. B, vol. 103

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.

Authors 6

1. Yen‐Ting Lin Aachen Institut für Theorie der Statistischen Physik

   Jülich Aachen Research Alliance · RWTH Aachen University

   Affiliation as printed

   Institut für Theorie der Statistischen Physik, RWTH Aachen University and JARA—Fundamentals of Future Information Technology, 52056 Aachen, Germany

2. Clara S. Weber Aachen Institut für Theorie der Statistischen Physik

   Jülich Aachen Research Alliance · RWTH Aachen University

   Affiliation as printed

   Institut für Theorie der Statistischen Physik, RWTH Aachen University and JARA—Fundamentals of Future Information Technology, 52056 Aachen, Germany

3. Dante Marvin Kennes Aachen Institut für Theorie der Statistischen Physik

   Jülich Aachen Research Alliance · Center for Free-Electron Laser Science · Max Planck Institute for the Structure and Dynamics of Matter · RWTH Aachen University

   Affiliation as printed

   Institut für Theorie der Statistischen Physik, RWTH Aachen University and JARA—Fundamentals of Future Information Technology, 52056 Aachen, Germany

   Max Planck Institute for the Structure and Dynamics of Matter, Center for Free Electron Laser Science, 22761 Hamburg, Germany

4. Mikhail Pletyukhov Aachen Institut für Theorie der Statistischen Physik

   Jülich Aachen Research Alliance · RWTH Aachen University

   Affiliation as printed

   Institut für Theorie der Statistischen Physik, RWTH Aachen University and JARA—Fundamentals of Future Information Technology, 52056 Aachen, Germany

5. Herbert Schoeller Aachen Institut für Theorie der Statistischen Physik

   Jülich Aachen Research Alliance · RWTH Aachen University

   Affiliation as printed

   Institut für Theorie der Statistischen Physik, RWTH Aachen University and JARA—Fundamentals of Future Information Technology, 52056 Aachen, Germany

6. V. Meden Aachen Institut für Theorie der Statistischen Physik

   Jülich Aachen Research Alliance · RWTH Aachen University

   Affiliation as printed

   Institut für Theorie der Statistischen Physik, RWTH Aachen University and JARA—Fundamentals of Future Information Technology, 52056 Aachen, Germany