Generating Exceptional Knots and Links with Arbitrary Braiding Topology
Fuente:
arXiv
Salvato in:
| Autori principali: | , , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2026
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866915853316915200 |
|---|---|
| author | Jiang, Bin Guo, Aolong Cai, Qilin Jiang, Jian-Hua |
| author_facet | Jiang, Bin Guo, Aolong Cai, Qilin Jiang, Jian-Hua |
| contents | Non-Hermitian systems host band degeneracies that are fundamentally distinct from those in Hermitian systems, most notably exceptional points (EPs) where both eigenvalues and eigenvectors coalesce. In three dimensional (3D) non-Hermitian systems, such degeneracies can form closed exceptional loops (ELs), whose global geometry can exhibit nontrivial knot and link structures. In this work, we present a universal and constructive framework for realizing knotted and linked ELs in 3D systems, establishing a direct correspondence between knot theory and non-Hermitian band degeneracies. Starting from an arbitrary knot or link specified by a braid representation, we systematically construct minimal two-band non-Hermitian Hamiltonians whose ELs faithfully realize the prescribed topology in momentum space, enabling a classification of non-Hermitian topological phases based on knot invariants such as braid words and Alexander polynomials. We show that these knotted ELs are generically stable and give rise to non-Hermitian metallic phases characterized by Seifert surfaces, reflecting the defective nature of exceptional degeneracies, in sharp contrast to nodal lines in Hermitian systems that typically require symmetry protection or fine-tuning. Furthermore, we demonstrate that knotted ELs can be continuously deformed and untied through controlled topological transitions driven by a single tuning parameter, providing a deterministic mechanism for manipulating knot topology in momentum space. We also propose an experimental realization in electro-acoustic systems, demonstrating the feasibility of observing knotted ELs through nonreciprocal coupling and tunable parameters. Our results establish knot and link topology as a natural classification scheme for non-Hermitian topological matter and suggest broad applicability in engineered platforms such as photonic, acoustic, and circuit-based systems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_04143 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Generating Exceptional Knots and Links with Arbitrary Braiding Topology Jiang, Bin Guo, Aolong Cai, Qilin Jiang, Jian-Hua Mesoscale and Nanoscale Physics Non-Hermitian systems host band degeneracies that are fundamentally distinct from those in Hermitian systems, most notably exceptional points (EPs) where both eigenvalues and eigenvectors coalesce. In three dimensional (3D) non-Hermitian systems, such degeneracies can form closed exceptional loops (ELs), whose global geometry can exhibit nontrivial knot and link structures. In this work, we present a universal and constructive framework for realizing knotted and linked ELs in 3D systems, establishing a direct correspondence between knot theory and non-Hermitian band degeneracies. Starting from an arbitrary knot or link specified by a braid representation, we systematically construct minimal two-band non-Hermitian Hamiltonians whose ELs faithfully realize the prescribed topology in momentum space, enabling a classification of non-Hermitian topological phases based on knot invariants such as braid words and Alexander polynomials. We show that these knotted ELs are generically stable and give rise to non-Hermitian metallic phases characterized by Seifert surfaces, reflecting the defective nature of exceptional degeneracies, in sharp contrast to nodal lines in Hermitian systems that typically require symmetry protection or fine-tuning. Furthermore, we demonstrate that knotted ELs can be continuously deformed and untied through controlled topological transitions driven by a single tuning parameter, providing a deterministic mechanism for manipulating knot topology in momentum space. We also propose an experimental realization in electro-acoustic systems, demonstrating the feasibility of observing knotted ELs through nonreciprocal coupling and tunable parameters. Our results establish knot and link topology as a natural classification scheme for non-Hermitian topological matter and suggest broad applicability in engineered platforms such as photonic, acoustic, and circuit-based systems. |
| title | Generating Exceptional Knots and Links with Arbitrary Braiding Topology |
| topic | Mesoscale and Nanoscale Physics |
| url | https://arxiv.org/abs/2603.04143 |