Parameter-dependent quantum systems often exhibit energy degeneracy points, whose comprehensive description naturally leads to the application of methods from singularity theory. A prime example is an electronic band structure where two energy levels coincide in a point of momentum space.  It may happen, and this case is our focus, that three or more levels coincide at a parameter point, called multifold degeneracy. For example, the Hamiltonian of a spinful particle in an external magnetic field has a (2s+1) -fold degeneracy for zero magnetic field, where s is the total spin. Upon a generic perturbation, such a multifold degeneracy point is dissolved into a set of Weyl points, that is, generic two-fold degeneracy points. We provide an upper bound to the number of Weyl points born from a multifold degeneracy point. Our work attempts to bridge two disciplines, quantum mechanics and singularity theory (algebraic geometry).

 

Joint work with György Frank, Dániel Varjas, András Pályi with a significant contribution of Alex Hof. 

https://arxiv.org/abs/2507.17485