Workshop 2025: Upper bound on the number of Weyl points born from a multifold degeneracy point

Session Information

Location: Lecture room F3213 - 19
Day: Wednesday, 14 May
Time: 18:00 - 19:00
Chairperson: -

Presentation Details

Presentation Type: Poster presentation
Title: Upper bound on the number of Weyl points born from a multifold degeneracy point
Abstract: Two-fold energy degeneracies with linear dispersion relation, often referred to as Weyl points, arise generically in the spectrum of a Hamiltonian that depends on three parameters.
Isolated multifold degeneracy points are less generic, but arise often, e.g., in band structures of three-dimensional crystalline materials, and in models of spin systems subject to a magnetic field. A generic perturbation dissolves such a multifold degeneracy point into an ensemble of Weyl points. We show that the number of Weyl points born from the $k$-fold degeneracy point has an upper bound given by the $k$th four-dimensional pyramidal number $dm(k) = k^2(k^2-1)/12$. We refer to this upper bound as the `birth quota' of the $k$-fold degeneracy point. Our results yield a strong result for the perturbation theory of multifold degeneracies in general, and in particular, provide clear predictions for the perturbation-induced dissolution of multifold degeneracies in band structures.

Presenter

Dr Gergő Pintér
HUN-REN-BME-BCE Quantum Technology Research Group, Műegyetem rkp. 3., H-1111 Budapest, Hungary | Hungary

Authors

1. Gergő Pintér | HUN-REN-BME-BCE Quantum Technology Research Group, Műegyetem rkp. 3., H-1111 Budapest, Hungary
2. György Frank | -
3. András Pályi | HUN-REN-BME-BCE Quantum Technology Research Group, Műegyetem rkp. 3., H-1111 Budapest, Hungary
4. Dániel Varjas | HUN-REN-BME-BCE Quantum Technology Research Group, Műegyetem rkp. 3., H-1111 Budapest, Hungary
5. Alexander Hof | HUN-REN Alfréd Rényi Institute of Mathematics