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.

Figures (2)

• Figure 1: Single-particle occupations for the $\nu{=}2$ integer quantum Hall state for $N{=}8$ electrons, showing different choices of the empty SLL orbital (labeled by $m$).
• Figure 2: QHs $1$ and $4$ are initially placed at distance of $r{=}R{/}3$ from the origin at polar angles $\theta{=}0$ and $\pi$, respectively, where $R{=}\sqrt{2N{/}\nu}$. QHs $2$ and $3$ are fixed at $r{=}2R{/}3$ at $\theta{=}0$ and $\pi$, respectively.