General procedure for determining braiding and statistics of anyons using entanglement interferometry

Abstract

Recently, it was argued that the braiding and statistics of anyons in a two-dimensional topological phase can be extracted by studying the quantum entanglement of the degenerate ground-states on the torus. This construction either required a lattice symmetry (such as $\pi /2$ rotation) or tacitly assumed that the `minimum entanglement states' (MESs) for two different bipartitions can be uniquely assigned quasiparticle labels. Here we describe a procedure to obtain the modular $\mathcal{S}$ matrix, which encodes the braiding statistics of anyons, which does not require making any of these assumptions. Our strategy is to compare MESs of three independent entanglement bipartitions of the torus, which leads to a unique modular $\mathcal{S}$. This procedure also puts strong constraints on the modular $\mathcal{T}$ and $\mathcal{U}$ matrices without requiring any symmetries, and in certain special cases, completely determines it. Our method applies equally to Abelian and non-Abelian topological phases.

9 pages, 3 figures

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• Microscopic definitions of anyon data
• Ising Anyons in Frustration-Free Majorana-Dimer Models
• Measuring space-group symmetry fractionalization in Z${}_2$ spin liquids
• Entanglement entropy of (3+1)D topological orders with excitations
• Modular transformations through sequences of topological charge projections
• Determining non-Abelian topological order from infinite projected entangled pair states
• Kohn-Sham Density Functional Theory of Abelian Anyons
• Determining topological order from infinite projected entangled pair states
• Universal edge information from wave-function deformation
• Detecting topological order from modular transformations of ground states on the torus
• Single-shot quantum measurements sketch quantum many-body states
• Remote detectability from entanglement bootstrap I: Kirby's torus trick