Eigenvalue knots and their isotopic equivalence in three-state non-Hermitian systems

Zhen Li, Kun Ding*, Guancong Ma*

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

5 Citations (Scopus)


The spectrum of a non-Hermitian system generically forms a two-dimensional complex Riemannian manifold with a distinct topology from the underlying parameter space. This spectral topology permits eigenvalue trajectories to braid into knots. In this paper, through the analyses of encircling loops, exceptional points, and their topology, we uncover the necessary considerations for constructing eigenvalue knots and establish their relation to the 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 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.

Original languageEnglish
Article number023038
Number of pages12
JournalPhysical Review Research
Issue number2
Publication statusPublished - Apr 2023

Scopus Subject Areas

  • Physics and Astronomy(all)


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