RKKY interaction in one-dimensional flat-band lattices

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 n...

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Bibliographic Details
Published in:arXiv.org 2023-11
Main Authors: Laubscher, Katharina, Weber, Clara S, Hünenberger, Maximilian, Schoeller, Herbert, Kennes, Dante M, Loss, Daniel, Klinovaja, Jelena
Format: Article
Language:English
Subjects:
Diamonds
Energy gap
Perturbation theory
Online Access:Get full text
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Summary: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.
ISSN:2331-8422
DOI:10.48550/arxiv.2210.10025