Harmonic generation with topological edge states and electron-electron interaction

TL;DR

This paper demonstrates that the significant difference in harmonic generation spectra between trivial and topological phases in the SSH model persists even when electron-electron interactions are included, using exact diagonalization of finite chains.

Contribution

It shows that the impact of topological edge states on harmonic generation remains robust with electron-electron interactions, modeled via a Hubbard term, and can be explained with simplified few-level models.

Findings

Harmonic yield differs greatly between topological and trivial phases.

The effect persists with electron-electron interactions included.

Few-level models can reproduce the main spectral differences.

Abstract

It has been found previously that the presence or absence of topological edge states in the Su-Schrieffer-Heeger (SSH) model has a huge impact on harmonic generation spectra. More specifically, the yield of harmonics for harmonic orders that correspond to photon energies below the band gap is many orders of magnitude different in the trivial and topological phase. It is shown in this work that this effect is still present if electron-electron interaction is taken into account, i.e., if a Hubbard term is added to the SSH Hamiltonian. To that end, finite SSH-Hubbard chains at half filling are considered that are short enough to be accessible to exact diagonalization but already showing edge states in the topological phase. We show that the huge difference in the harmonic yield between the trivial and the topological phase can be reproduced with few-level models employing only the many-body ground state and a few excited many-body states.