Unveiling Anyon Fusion in Quantum Hall Systems from Microscopic Principles with Gerardo Ortiz

Establishing the fusion rules of anyonic quasiparticles in fractional quantum Hall fluids is essential for understanding their underlying topological order. Building on the conjecture that key topological properties are encoded in the “DNA” of candidate many-body wave functions—that is, the pattern of dominant orbital occupations restricted to a finite number of lowest Landau levels—we propose a combinatorial framework that derives these fusion rules directly from microscopic data. By extending Schrieffer’s counting argument and introducing equivalences for topological excitations, our framework provides a unified route to the fusion rules for both Abelian and non-Abelian excitations. This approach elucidates the emergence of topological features from first principles in both fermionic and bosonic systems.

This lecture was made possible by the William C. Ferguson Fund.