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arXiv · 2306.13056

Gain-loss-induced non-Abelian Bloch braids

B. Midya
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Abstract

Onsite gain-loss-induced topological braiding principle of non-Hermitian energy bands is theoretically formulated in multiband lattice models with Hermitian hopping amplitudes. Braid phase transition occurs when the gain-loss parameter is tuned across exceptional point degeneracy. Laboratory realizable effective-Hamiltonians are proposed to realize braid groups $\mathbb{B}_2$ and $\mathbb{B}_3$ of two and three bands, respectively. While $\mathbb{B}_2$ is trivially Abelian, the group $\mathbb{B}_3$ features non-Abelian braiding and energy permutation originating from the collective behavior of multiple exceptional points. Phase diagrams with respect to lattice parameters to realize braid group generators and their non-commutativity are shown. The proposed theory is conducive to synthesizing exceptional materials for applications in topological computation and information processing.

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B. Midya. 2023-06-22. Gain-loss-induced non-Abelian Bloch braids. https://doi.org/10.1063/5.0164009

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