Unveiling Topological Fusion in Quantum Hall Systems from Microscopic Principles

TL;DR

This paper introduces a combinatorial framework to derive fusion rules of anyonic quasiparticles in fractional quantum Hall systems directly from microscopic wave functions, linking topological properties to orbital occupation patterns.

Contribution

It extends Schrieffer's counting argument and develops a unified method to determine fusion rules for both Abelian and non-Abelian excitations from microscopic data.

Findings

Provides a microscopic derivation of fusion rules in quantum Hall systems.

Unifies the understanding of topological excitations in fermionic and bosonic systems.

Connects orbital occupation patterns to topological properties.

Abstract

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 classes of 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.