Synthetic non-Abelian gauge fields for non-Hermitian systems

Abstract

Non-Abelian gauge fields are versatile tools for synthesizing topological phenomena but have so far been mostly studied in Hermitian systems, where gauge flux has to be defined from a closed loop in order for gauge fields, whether Abelian or non-Abelian, to become physically meaningful. We show that this condition can be relaxed in non-Hermitian systems by proposing and studying a generalized Hatano--Nelson model with imbalanced non-Abelian hopping. Despite lacking gauge flux in one dimension, non-Abelian gauge fields create rich non-Hermitian topological consequences. Under only nearest-neighbor coupling, non-Abelian gauge fields enable Hopf-link bulk braiding topology, whose phase transition accompanies the emergence of exceptional points (EPs). At both ends of an open chain, non-Abelian gauge fields lead to the simultaneous presence of non-Hermitian skin modes, whose population can be effectively tuned. Asymptotic analysis shows that this tuning mechanism stems from the interplay between the Abelian Hatano--Nelson coupling and effective high-order hopping, which becomes substantial near the EP phase transition condition. The predicted non-Hermitian phenomena, enabled by non-Abelian gauge fields, could be realized in synthetic dimensional optical platforms such as time-multiplexed photonic mesh lattices and driven ring resonators.

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Cited by in corpus (17)

• Non-Abelian lattice gauge fields in the photonic synthetic frequency dimension
• A comprehensive review on developments of synthetic dimensions
• Higher-Order Topological Insulators via Momentum-Space Nonsymmorphic Symmetries
• Braiding Topology of Non-Hermitian Open-Boundary Bands
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• Implementing non-Abelian Hatano-Nelson model in electric circuits
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• Non-Abelian gauge field optics in the time domain
• Topological quantum electrodynamics in synthetic non-Abelian gauge fields