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We show the existence of invariant energy levels in a Kondo lattice model on an isolated complete graph, such as a triangle and a tetrahedron. These energy levels always have fixed eigenenergies t ± J/2, irrespective of the configuration of localized moments (t is the transfer integral of conduction electrons and J is the spin-charge coupling constant). We also extend the analysis to geometrically frustrated lattices by using the complete graphs as basic building blocks. We show that the<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1310.4580v1">arXiv:1310.4580v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/hfewgc7i35fppb4uyjg3qhsovq">fatcat:hfewgc7i35fppb4uyjg3qhsovq</a> </span>
more »... ction rule for the invariant energy levels leads to the existence condition of localized states, if the model is defined on the triangle-based line graphs, such as a kagome lattice. We further propose a procedure of engineering isolated flat bands with broken time-reversal symmetry, which are separated from other dispersive bands with finite energy gaps.
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