What the study found
The study finds an upper bound on the number of Weyl points, which are generic twofold degeneracy points, that can arise when a multifold degeneracy point splits in a quantum system. The authors also relate this problem to singularities in the space of complex matrices.
Why the authors say this matters
The authors say the work helps connect physics and mathematics by using singularity theory and local algebraic geometry to study energy degeneracies in quantum systems. They also state that the paper surveys examples from quantum systems and condensed-matter physics to support this bridge between the two fields.
What the researchers tested
The researchers studied parameter-dependent quantum systems in which three or more energy levels coincide at a point, called a multifold degeneracy. They described the geometric degeneracy variety in the space of complex matrices and computed its multiplicity at certain singular points, along with the multiplicity of holomorphic map germs with respect to this variety.
What worked and what didn't
The approach produced an upper bound for the number of Weyl points born from a multifold degeneracy point. The abstract does not report a negative result or a comparison showing that another method failed.
What to keep in mind
The abstract does not give the actual upper bound value in the summary provided. It also does not state experimental data, specific systems analyzed in detail, or limitations beyond the scope of the mathematical framework described.
Key points
- A multifold degeneracy point can split into multiple Weyl points under a generic perturbation.
- The authors provide an upper bound on how many Weyl points can arise from that splitting.
- Their calculation uses the degeneracy variety in the space of complex matrices.
- They compute multiplicities at singular points and for holomorphic map germs.
- The paper aims to connect quantum physics with singularity theory and local algebraic geometry.
Disclosure
- Research title:
- Multifold quantum degeneracies can produce bounded numbers of Weyl points
- Authors:
- György Frank, Gergő Pintér, Dániel Varjas, András Pályi
- Institutions:
- Budapest University of Technology and Economics, Budapest University of Technology and Economics, Budapest University of Technology and Economics, Budapest University of Technology and Economics, Complexity and Topology in Quantum Matter, Leibniz Institute for Solid State and Materials Research
- Publication date:
- 2026-04-20
- OpenAlex record:
- View
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