SUSY transformation as the coupler of non-interacting systems

Quasi-one-dimensional chains of atoms can be effectively described by one-dimensional Dirac-type equation. Crystal structure of the chain is reflected by pseudo-spin of the quasi-particles. In the article, we present a simple framework where supersymmetric transformation is utilized to generate an interaction between two, initially non-interacting systems described by pseudo-spin-one Dirac-type equation. In the presented example, the transformation converts two asymptotically non-interacting atomic chains into a saw chain locally. The model possesses a flat band whose energy can be fine-tuned deliberately.