RKKY interaction in one-dimensional flat-band lattices

TL;DR

This paper investigates how flat bands in one-dimensional lattices influence the RKKY interaction between magnetic impurities, revealing unique features not explained by traditional theories, and compares analytical methods with exact numerical calculations.

Contribution

It demonstrates the limitations of conventional RKKY approximations in flat-band systems and highlights the importance of degenerate perturbation theory for accurate descriptions.

Findings

Flat bands cause peculiar RKKY features.

Degenerate perturbation theory works with an energy gap.

Non-perturbative methods are needed without a gap.

Abstract

We study the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction between two classical magnetic impurities in one-dimensional lattice models with flat bands. As two representative examples, we pick the stub lattice and the diamond lattice at half filling. We first calculate the exact RKKY interaction numerically and then compare our data to results obtained via different analytical techniques. In both our examples, we find that the RKKY interaction exhibits peculiar features that can directly be traced back to the presence of a flat band in the energy spectrum. Importantly, these features are not captured by the conventional RKKY approximation based on non-degenerate perturbation theory. Instead, we find that degenerate perturbation theory correctly reproduces our exact results if there is an energy gap between the flat and the dispersive bands, while a non-perturbative approach becomes necessary in the absence of a gap.