Entanglement spectroscopy of non-Abelian anyons: Reading off quantum dimensions of individual anyons

TL;DR

This paper demonstrates that the entanglement spectrum of topological systems with non-Abelian anyons reveals universal ratios linked to quantum dimensions, providing a potential experimental method to identify topological order.

Contribution

It establishes a universal relationship between entanglement spectrum eigenvalues and anyonic quantum dimensions, extending known degeneracies in topological states.

Findings

Eigenvalue ratios within symmetry multiplets are universal and determined by quantum dimensions.

The entanglement spectrum degeneracies are generalized for non-Abelian topological order.

Experimental detection may be feasible using multicopy schemes in Majorana wires.

Abstract

We study the entanglement spectrum of topological systems hosting non-Abelian anyons. Akin to energy levels of a Hamiltonian, the entanglement spectrum is composed of symmetry multiplets. We find that the ratio between different eigenvalues within one multiplet is universal and is determined by the anyonic quantum dimensions. This result is a consequence of the conservation of the total topological charge. For systems with non-Abelian topological order, this generalizes known degeneracies of the entanglement spectrum, which are hallmarks of topological states. Experimental detection of these entanglement spectrum signatures may become possible in Majorana wires using multicopy schemes, allowing the measurement of quantum entanglement and its symmetry resolution.