Non-Abelian fusion and braiding in many-body parton states

Abstract: Fractional quantum Hall (FQH) states host fractionally charged anyons with exotic exchange statistics. Of particular interest are FQH phases supporting non-Abelian anyons, which can encode topologically protected quantum information. In this work, we construct quasihole bases for a broad family of non-Abelian FQH states using parton wave functions, which reproduces the fusion-space dimensionality expected from their underlying conformal field theory, consistent with level-rank duality across the parton family. As an application, we numerically compute braiding matrices for representative parton states for large systems, providing a general framework for diagnosing non-Abelian characteristics in candidate FQH states.