Measuring the knot of non-Hermitian degeneracies and non-commuting braids

Patil, Yogesh Sharad; Höller, J.; Henry, Parker A.; Guria, Chitres; Zhang, Yiming; Jiang, Luyao; Kralj, Nenad; Read, N.; Harris, Jack

doi:10.1038/s41586-022-04796-w

Cited by 51 publications

(35 citation statements)

References 57 publications

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“…[ 179 ] For even higher N‐level systems, it has been proven that through controlled loops, that is, the parameters are varied in the Riemann surfaces in controlled manners, eigenvalues are braided. [ 180 ] For

N\gt 2

, the braids of the eigenvalues in general form non‐Abelian groups and therefore give rise to a variety of novel topological structures of knots and links in parameter spaces. [ 180 ]…”

Section: Non‐hermitian Topological Physicsmentioning

confidence: 99%

Various topological phases and their abnormal effects of topological acoustic metamaterials

Chen

et al. 2023

Interdisciplinary Materials

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The last 20 years have witnessed growing impacts of the topological concept on the branches of physics, including materials, electronics, photonics, and acoustics. Topology describes objects with some global invariant property under continuous deformation, which in mathematics could date back to the 17th century and mature in the 20th century. In physics, it successfully underpinned the physics of the Quantum Hall effect in 1984. To date, topology has been extensively applied to describe topological phases in acoustic metamaterials. As artificial structures, acoustic metamaterials could be well theoretically analyzed, on‐demand designed, and easily fabricated by modern techniques, such as three‐dimensional printing. Some new theoretical topological models were first discovered in acoustic metamaterials analogous to electronic counterparts, associated with novel effects for acoustics closer to applications. In this review, we focused on the concept of topology and its realization in airborne acoustic crystals, solid elastic phononic crystals, and surface acoustic wave systems. We also introduced emerging concepts of non‐Hermitian, higher‐order, and Floquet topological insulators in acoustics. It has been shown that the topology theory has such a powerful generality that among the disciplines from electron to photon and phonon, from electronic to photonics and acoustics, from acoustic topological theory to acoustic devices, could interact and be analogous to fertilize fantastic new ideas and prototype devices, which might find applications in acoustic engineering and noise‐vibration control engineering in the near future.

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N\gt 2

, the braids of the eigenvalues in general form non‐Abelian groups and therefore give rise to a variety of novel topological structures of knots and links in parameter spaces. [ 180 ]…”

Section: Non‐hermitian Topological Physicsmentioning

confidence: 99%

Various topological phases and their abnormal effects of topological acoustic metamaterials

Chen

et al. 2023

Interdisciplinary Materials

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“…This subtlety is showcased in two simple models below. Note that the theory of non-Hermitian bands in connection with Lindbladian dynamics is still under construction and the following discussion is far from exhaustive, see [81,82,83,84,85,86,87].…”

Section: Non-hermitian Band Theorymentioning

confidence: 99%

“…Recent literature has understood this sort of atypical feature of non-Hermitian band theory in the context of braids and knots [84,85,86,87]. The eigenvalues of the dynamic matrix H(k) define paths in the complex plain parametrized by k. Due to the periodicity of k, the paths must close and so define loops, which can braid together and link up.…”

Section: Non-hermitian Band Theorymentioning

confidence: 99%

Field Theory of Many-Body Lindbladian Dynamics

Thompson¹,

Kamenev²

2023

Preprint

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We review and further develop the Keldysh functional integral technique for the study of Lindbladian evolution of many-body driven-dissipative quantum systems. A systematic and pedagogical account of the dynamics of generic bosonic and fermionic Lindbladians is presented. Our particular emphasis is on unique properties of the stationary distribution function, determined by the Lyapunov equation. This framework is applied to study examples of Lindbladian dynamics in the context of band theory, disorder, collisionless collective modes, and mean-field theory.

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“…As a bonus, our framework, in an intuitive and exact way, solves the starting-point problem in stroboscopic encircling multiple EPs [74,75]. Different from the homotopy/knot theory of separable bands [58][59][60], or an isolated EP [61,76] without a base point, the based-path is necessary to account for the interplay of multiple EPs. Choosing another base point ends up with a conjugate braid invariant [77].…”

Section: (D) (Top Panel)mentioning

confidence: 99%