Identifying Non-Abelian Topological Order through Minimal Entangled States

TL;DR

This study uses exact diagonalization to identify non-Abelian topological order by analyzing minimal entangled states and their modular matrices, revealing quasiparticle statistics and fusion rules.

Contribution

It demonstrates that minimal entangled states encode complete topological information, including quasiparticle types and their fusion rules, in lattice models.

Findings

Identified multiple minimal entangled states in non-Abelian topological phases.

Extracted modular S matrices confirming Majorana and Fibonacci quasiparticle statistics.

Showed MESs encode full topological order information.

Abstract

The topological order is equivalent to the pattern of long-range quantum entanglements, which cannot be measured by any local observable. Here we perform an exact diagonalization study to establish the non-Abelian topological order through entanglement entropy measurement. We focus on the quasiparticle statistics of the non-Abelian Moore-Read and Read-Rezayi states on the lattice boson models. We identify multiple independent minimal entangled states (MESs) in the groundstate manifold on a torus. The extracted modular $\mathcal{S}$ matrix from MESs faithfully demonstrates the Majorana quasiparticle or Fibonacci quasiparticle statistics, including the quasiparticle quantum dimensions and the fusion rules for such systems. These findings support that MESs manifest the eigenstates of quasiparticles for the non-Abelian topological states and encode the full information of the topological order.