Non-Hermitian eigenvalue knots and their isotopic equivalence

Abstract

The spectrum of a non-Hermitian system generically forms a two-dimensional complex Riemannian manifold with distinct topology from the underlying parameter space. Spectral topology permits parametric loops to map the affiliated eigenvalue trajectories into knots. In this work, through analyzing exceptional points and their topology, we uncover the necessary considerations for constructing eigenvalue knots and establish their relation to spectral topology. Using an acoustic system with two periodic synthetic dimensions, we experimentally realize several knots with braid index 3. In addition, by highlighting the role of branch cuts on the eigenvalue manifolds, we show that eigenvalue knots produced by homotopic parametric loops are isotopic such that they can deform into one another by type-II or type-III Reidemeister moves. Our results not only provide a general recipe for constructing eigenvalue knots but also expand the current understanding of eigenvalue knots by showing that they contain information beyond that of the spectral topology.

References in corpus (5)

• Making Sense of Non-Hermitian Hamiltonians
• The physics of exceptional points
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• Topological energy braiding of the non-Bloch bands
• Experimental Realization of Non-Abelian Permutations in a Three-State Non-Hermitian System

Cited by in corpus (9)

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• Higher-order Skin Effect through a Hermitian-non-Hermitian Correspondence and Its Observation in an Acoustic Kagome Lattice
• Versatile Braiding of Non-Hermitian Topological Edge States
• Implementing non-Abelian Hatano-Nelson model in electric circuits
• Gain-loss-induced non-Abelian Bloch braids
• Entanglement manifestation of knot topology in a non-Hermitian lattice
• Braiding of dynamical eigenvalues of Hermitian bosonic Kitaev chains